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Вариант 10, страница 69 - гдз по физике 9 класс дидактические материалы Марон, Марон
Авторы: Марон А. Е., Марон Е. А.
Тип: Дидактические материалы
Издательство: Просвещение
Год издания: 2022 - 2026
Уровень обучения: базовый
Цвет обложки: белый изображена башня
ISBN: 978-5-09-111414-0
Популярные ГДЗ в 9 классе
Самостоятельные работы. СР-5. Прямолинейное равноускоренное движение. Графические задачи - страница 69.
App\Models\Task {#1024 // resources/views/models/task/default.blade.php #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1428619 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "69" "field_page_end" => null "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp05-10" "field_display_title" => "Вариант 10" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#331 #items: [] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1029 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1026 #items: array:1 [ 0 => App\Models\Branch {#342 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1428174 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Самостоятельные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1023 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "53" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#333 #items: array:1 [ 0 => App\Models\Book {#1033 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 894 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1030 #items: array:1 [ 0 => App\Models\Term {#1032 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #original: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1034 #items: array:1 [ 0 => App\Models\Term {#1035 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "field_translit" => "devjatyj" ] #original: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "field_translit" => "devjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1036 #items: array:1 [ 0 => App\Models\Term {#1037 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #original: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1038 #items: array:2 [ 0 => App\Models\Term {#1039 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 5107 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Марон" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Абрам" "field_patronymic" => "Евсеевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 5107 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Марон" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Абрам" "field_patronymic" => "Евсеевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1040 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 5108 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Марон" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Евгений" "field_patronymic" => "Абрамович" "field_surname_rp" => null ] #original: array:12 [ "id" => 5108 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Марон" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Евгений" "field_patronymic" => "Абрамович" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1041 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1042 #items: array:1 [ 0 => App\Models\Term {#1043 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6510 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Дидактические материалы" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "дидактические материалы" "field_creative_case" => "дидактическими материалами" "field_dative_case" => "дидактическим материалам" "field_genitive_case" => "дидактических материалов" "field_nominative_case" => "дидактические материалы" "field_prepositional_case" => "дидактических материалах" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "didakticheskie materialy" ] #original: array:10 [ "id" => 6510 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Дидактические материалы" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "дидактические материалы" "field_creative_case" => "дидактическими материалами" "field_dative_case" => "дидактическим материалам" "field_genitive_case" => "дидактических материалов" "field_nominative_case" => "дидактические материалы" "field_prepositional_case" => "дидактических материалах" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "didakticheskie materialy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1044 #items: array:1 [ 0 => App\Models\Term {#1045 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "rossiya" ] #original: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "rossiya" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1046 #items: array:1 [ 0 => App\Models\Term {#1047 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "moskva" ] #original: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "moskva" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1048 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1049 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1050 #items: array:1 [ 0 => App\Models\Term {#1051 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 38 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "базовый" "field_cases" => array:6 [ "field_accusative_case" => "базовый" "field_creative_case" => "базовым" "field_dative_case" => "базовому" "field_genitive_case" => "базового" "field_nominative_case" => "базовый" "field_prepositional_case" => "базовом" ] "field_translit" => "bazovyy" ] #original: array:6 [ "id" => 38 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "базовый" "field_cases" => array:6 [ "field_accusative_case" => "базовый" "field_creative_case" => "базовым" "field_dative_case" => "базовому" "field_genitive_case" => "базового" "field_nominative_case" => "базовый" "field_prepositional_case" => "базовом" ] "field_translit" => "bazovyy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1052 #items: array:1 [ 0 => App\Models\Term {#1053 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 25 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (новый)" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_color" => "красный" "field_end_year" => "2027" "field_start_year" => "2023" "field_translit" => "fgos" "field_type" => "новый" ] #original: array:10 [ "id" => 25 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (новый)" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_color" => "красный" "field_end_year" => "2027" "field_start_year" => "2023" "field_translit" => "fgos" "field_type" => "новый" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publication_number" => "3" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1054 #items: array:1 [ 0 => App\Models\Term {#1055 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 34 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "переработанное" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "pererabotannoe" ] #original: array:6 [ "id" => 34 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "переработанное" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "pererabotannoe" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1056 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "изображена башня" "field_publication_year" => "2022" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "674" "field_priority" => null "field_default_folder" => "/fizika_09/maron-dm/" "field_isbn" => "978-5-09-111414-0" "field_cover" => array:1 [ 0 => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880" "alt" => "" "width" => "1888" "height" => "2427" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1057 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1058 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1059 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1060 #items: array:1 [ 0 => App\Models\Term {#1061 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 45 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "белый" "field_cases" => array:6 [ "field_accusative_case" => "белый" "field_creative_case" => "белым" "field_dative_case" => "белому" "field_genitive_case" => "белого" "field_nominative_case" => "белый" "field_prepositional_case" => "белом" ] "field_translit" => "belyy" ] #original: array:6 [ "id" => 45 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "белый" "field_cases" => array:6 [ "field_accusative_case" => "белый" "field_creative_case" => "белым" "field_dative_case" => "белому" "field_genitive_case" => "белого" "field_nominative_case" => "белый" "field_prepositional_case" => "белом" ] "field_translit" => "belyy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 556 "class_subject" => 493 ] ] #original: array:50 [ "id" => 894 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1030} "field_class" => Illuminate\Database\Eloquent\Collection {#1034} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1036} "field_author" => Illuminate\Database\Eloquent\Collection {#1038} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1041} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1042} "field_country" => Illuminate\Database\Eloquent\Collection {#1044} "field_city" => Illuminate\Database\Eloquent\Collection {#1046} "field_series" => Illuminate\Database\Eloquent\Collection {#1048} "field_umk" => Illuminate\Database\Eloquent\Collection {#1049} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1050} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1052} "field_publication_number" => "3" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1054} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1056} "field_under_the_edition_degree" => null "field_cover_description" => "изображена башня" "field_publication_year" => "2022" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "674" "field_priority" => null "field_default_folder" => "/fizika_09/maron-dm/" "field_isbn" => "978-5-09-111414-0" "field_cover" => array:1 [ 0 => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880" "alt" => "" "width" => "1888" "height" => "2427" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1057} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1058} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1059} "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1060} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 556 "class_subject" => 493 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1062 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1428174 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Самостоятельные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1023} "field_page_start" => "53" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#333} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1062} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1063 #items: array:2 [ 0 => App\Models\Branch {#1064 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1428174 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Самостоятельные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1065 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "53" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1066 #items: array:1 [ 0 => App\Models\Book {#1033} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1067 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1428174 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Самостоятельные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1065} "field_page_start" => "53" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1066} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1067} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Branch {#1068 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1428179 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "СР-5. Прямолинейное равноускоренное движение. Графические задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1069 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "64" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1070 #items: array:1 [ 0 => App\Models\Book {#1033} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1071 #items: array:1 [ 0 => App\Models\Branch {#342} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1428179 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "СР-5. Прямолинейное равноускоренное движение. Графические задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1069} "field_page_start" => "64" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1070} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1071} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1072 #items: array:2 [ 0 => App\Models\Element {#1073 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 1682934 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1074 #items: array:1 [ 0 => App\Models\Edition {#1075 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5992 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1076 #items: array:1 [ 0 => App\Models\Term {#1077 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1078 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1079 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1080 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 5992 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1076} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1078} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1079} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1080} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1428619" "type" => "task" ] "text" => "<p><strong>1.</strong> Заполните таблицу, используя график скорости движения тела (рис. 112).</p><p>$v, м/с$</p><p>Начальная скорость $v_0$, м/с</p><p>Ускорение $\text{a}$, м/$с^2$</p><p>Уравнение скорости</p><p>Уравнение перемещения</p><p>Характер движения тела</p><p>$t, с$</p><p>Рис. 112</p><p><strong>2.</strong> Дано уравнение движения тела: $x = -2 + t + 2t^2$ (м). Заполните таблицу и постройте график скорости движения тела.</p><p>Начальная координата $x_0$, М</p><p>Начальная скорость $v_0$, м/с</p><p>Ускорение $\text{a}$, м/$с^2$</p><p>Уравнение скорости</p><p>Уравнение перемещения</p><p>Характер движения тела</p>" "img" => array:1 [ 0 => array:5 [ "name" => "10-1.jpg" "alt" => null "width" => "1491" "height" => 1093 "path" => "/media/fizika_09/maron-dm/0-cp05/10-1.webp?ts=1758964220" ] ] ] #original: array:7 [ "id" => 1682934 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1074} "task" => array:2 [ "refs" => "1428619" "type" => "task" ] "text" => "<p><strong>1.</strong> Заполните таблицу, используя график скорости движения тела (рис. 112).</p><p>$v, м/с$</p><p>Начальная скорость $v_0$, м/с</p><p>Ускорение $\text{a}$, м/$с^2$</p><p>Уравнение скорости</p><p>Уравнение перемещения</p><p>Характер движения тела</p><p>$t, с$</p><p>Рис. 112</p><p><strong>2.</strong> Дано уравнение движения тела: $x = -2 + t + 2t^2$ (м). Заполните таблицу и постройте график скорости движения тела.</p><p>Начальная координата $x_0$, М</p><p>Начальная скорость $v_0$, м/с</p><p>Ускорение $\text{a}$, м/$с^2$</p><p>Уравнение скорости</p><p>Уравнение перемещения</p><p>Характер движения тела</p>" "img" => array:1 [ 0 => array:5 [ "name" => "10-1.jpg" "alt" => null "width" => "1491" "height" => 1093 "path" => "/media/fizika_09/maron-dm/0-cp05/10-1.webp?ts=1758964220" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Element {#1081 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1730636 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1082 #items: array:1 [ 0 => App\Models\Edition {#1083 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 6313 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1084 #items: array:1 [ 0 => App\Models\Term {#1085 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1086 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1087 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1088 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6313 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1084} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1086} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1087} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1088} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1428619" "type" => "task" ] "text" => "<p><strong>1.</strong> Для заполнения таблицы необходимо проанализировать представленный график зависимости скорости от времени $v(t)$.</p><p><strong>Начальная скорость $v_0$, м/с</strong></p><p>Начальная скорость – это значение скорости в момент времени $t = 0$. Из графика видно, что линия зависимости скорости от времени проходит через начало координат, следовательно, начальная скорость тела $v_0 = 0$ м/с.</p><p><strong>Ускорение $\text{a}$, м/с²</strong></p><p>График скорости является прямой линией, что свидетельствует о равноускоренном движении. Ускорение $\text{a}$ постоянно и может быть найдено как тангенс угла наклона графика к оси времени. Для этого выберем на графике произвольную точку, например, с координатами $t = 4$ с и $v = 10$ м/с.</p><p>$a = \frac{\Delta v}{\Delta t} = \frac{v - v_0}{t - 0} = \frac{10 \text{ м/с} - 0 \text{ м/с}}{4 \text{ с}} = 2.5 \text{ м/с}^2$.</p><p><strong>Уравнение скорости</strong></p><p>Общий вид уравнения скорости для равноускоренного движения: $v(t) = v_0 + at$. Подставим найденные значения $v_0$ и $\text{a}$:</p><p>$v = 0 + 2.5t \Rightarrow v = 2.5t$.</p><p><strong>Уравнение перемещения</strong></p><p>Общий вид уравнения перемещения для равноускоренного движения: $s(t) = v_0t + \frac{at^2}{2}$. Подставим наши значения:</p><p>$s = 0 \cdot t + \frac{2.5t^2}{2} \Rightarrow s = 1.25t^2$.</p><p><strong>Характер движения тела</strong></p><p>Поскольку начальная скорость равна нулю ($v_0 = 0$), а ускорение постоянно и положительно ($a = 2.5 \text{ м/с}^2$), движение является прямолинейным равноускоренным из состояния покоя.</p><p>Заполненная таблица:</p><div class="table-wrap"><table border="1" style="border: 1px solid rgb(0, 0, 0);"><thead><tr><th style="border: 1px solid rgb(0, 0, 0);">Начальная скорость $v_0$, м/с</th><th style="border: 1px solid rgb(0, 0, 0);">Ускорение $\text{a}$, м/с²</th><th style="border: 1px solid rgb(0, 0, 0);">Уравнение скорости</th><th style="border: 1px solid rgb(0, 0, 0);">Уравнение перемещения</th><th style="border: 1px solid rgb(0, 0, 0);">Характер движения тела</th></tr></thead><tbody><tr><td style="border: 1px solid rgb(0, 0, 0);">0</td><td style="border: 1px solid rgb(0, 0, 0);">2.5</td><td style="border: 1px solid rgb(0, 0, 0);">$v = 2.5t$</td><td style="border: 1px solid rgb(0, 0, 0);">$s = 1.25t^2$</td><td style="border: 1px solid rgb(0, 0, 0);">Прямолинейное равноускоренное движение из состояния покоя</td></tr></tbody></table></div><p><strong>Ответ:</strong> Значения для таблицы: начальная скорость $v_0 = 0$ м/с; ускорение $a = 2.5$ м/с²; уравнение скорости $v = 2.5t$; уравнение перемещения $s = 1.25t^2$; характер движения – прямолинейное равноускоренное движение из состояния покоя.</p><p><strong>2.</strong> <strong>Дано:</strong></p><p>Уравнение движения тела: $x = -2 + t + 2t^2$ (м).</p><p>Все величины даны в системе СИ.</p><p><strong>Найти:</strong></p><p>$x_0, v_0, a$, уравнение скорости, уравнение перемещения, характер движения; построить график скорости $v(t)$.</p><p><strong>Решение:</strong></p><p>Общий вид уравнения для равноускоренного прямолинейного движения: $x(t) = x_0 + v_0t + \frac{at^2}{2}$. Сравним это уравнение с данным в условии: $x = -2 + 1 \cdot t + 2t^2$.</p><p><strong>Начальная координата $x_0$, м</strong></p><p>Из сравнения уравнений следует, что начальная координата $x_0 = -2$ м.</p><p><strong>Начальная скорость $v_0$, м/с</strong></p><p>Коэффициент при $\text{t}$ соответствует начальной скорости, следовательно $v_0 = 1$ м/с.</p><p><strong>Ускорение $\text{a}$, м/с²</strong></p><p>Коэффициент при $t^2$ равен $\frac{a}{2}$. В данном уравнении он равен 2. Отсюда: $\frac{a}{2} = 2 \Rightarrow a = 4 \text{ м/с}^2$.</p><p><strong>Уравнение скорости</strong></p><p>Общая формула для скорости: $v(t) = v_0 + at$. Подставим найденные значения $v_0$ и $\text{a}$: $v = 1 + 4t$.</p><p><strong>Уравнение перемещения</strong></p><p>Общая формула для перемещения: $s(t) = v_0t + \frac{at^2}{2}$. Подставим наши значения: $s = 1 \cdot t + \frac{4t^2}{2} \Rightarrow s = t + 2t^2$.</p><p><strong>Характер движения тела</strong></p><p>Поскольку ускорение постоянно и положительно ($a = 4 \text{ м/с}^2$), движение является прямолинейным равноускоренным.</p><p>Заполненная таблица:</p><div class="table-wrap"><table border="1" style="border: 1px solid rgb(0, 0, 0);"><thead><tr><th style="border: 1px solid rgb(0, 0, 0);">Начальная координата $x_0$, м</th><th style="border: 1px solid rgb(0, 0, 0);">Начальная скорость $v_0$, м/с</th><th style="border: 1px solid rgb(0, 0, 0);">Ускорение $\text{a}$, м/с²</th><th style="border: 1px solid rgb(0, 0, 0);">Уравнение скорости</th><th style="border: 1px solid rgb(0, 0, 0);">Уравнение перемещения</th><th style="border: 1px solid rgb(0, 0, 0);">Характер движения тела</th></tr></thead><tbody><tr><td style="border: 1px solid rgb(0, 0, 0);">-2</td><td style="border: 1px solid rgb(0, 0, 0);">1</td><td style="border: 1px solid rgb(0, 0, 0);">4</td><td style="border: 1px solid rgb(0, 0, 0);">$v = 1 + 4t$</td><td style="border: 1px solid rgb(0, 0, 0);">$s = t + 2t^2$</td><td style="border: 1px solid rgb(0, 0, 0);">Прямолинейное равноускоренное движение</td></tr></tbody></table></div><p><strong>Построение графика скорости движения тела</strong></p><p>График зависимости скорости от времени $v(t)$ описывается уравнением $v = 1 + 4t$. Это линейная функция, её график — прямая линия. Для построения достаточно двух точек:</p><p>При $t=0$, $v = 1 + 4 \cdot 0 = 1$ м/с. Координаты первой точки (0; 1).</p><p>При $t=2$, $v = 1 + 4 \cdot 2 = 9$ м/с. Координаты второй точки (2; 9).</p><p>Для построения графика на координатной плоскости с осями $\text{t}$ (с) и $\text{v}$ (м/с) нужно отметить эти две точки и провести через них прямую линию.</p><p><strong>Ответ:</strong></p><p>Результаты расчетов сведены в таблицу: $x_0 = -2$ м, $v_0 = 1$ м/с, $a = 4$ м/с², уравнение скорости $v = 1 + 4t$, уравнение перемещения $s = t + 2t^2$, характер движения – прямолинейное равноускоренное. График скорости $v(t)$ — прямая линия, проходящая через точки (0 с; 1 м/с) и (2 с; 9 м/с).</p>" ] #original: array:6 [ "id" => 1730636 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1082} "task" => array:2 [ "refs" => "1428619" "type" => "task" ] "text" => "<p><strong>1.</strong> Для заполнения таблицы необходимо проанализировать представленный график зависимости скорости от времени $v(t)$.</p><p><strong>Начальная скорость $v_0$, м/с</strong></p><p>Начальная скорость – это значение скорости в момент времени $t = 0$. Из графика видно, что линия зависимости скорости от времени проходит через начало координат, следовательно, начальная скорость тела $v_0 = 0$ м/с.</p><p><strong>Ускорение $\text{a}$, м/с²</strong></p><p>График скорости является прямой линией, что свидетельствует о равноускоренном движении. Ускорение $\text{a}$ постоянно и может быть найдено как тангенс угла наклона графика к оси времени. Для этого выберем на графике произвольную точку, например, с координатами $t = 4$ с и $v = 10$ м/с.</p><p>$a = \frac{\Delta v}{\Delta t} = \frac{v - v_0}{t - 0} = \frac{10 \text{ м/с} - 0 \text{ м/с}}{4 \text{ с}} = 2.5 \text{ м/с}^2$.</p><p><strong>Уравнение скорости</strong></p><p>Общий вид уравнения скорости для равноускоренного движения: $v(t) = v_0 + at$. Подставим найденные значения $v_0$ и $\text{a}$:</p><p>$v = 0 + 2.5t \Rightarrow v = 2.5t$.</p><p><strong>Уравнение перемещения</strong></p><p>Общий вид уравнения перемещения для равноускоренного движения: $s(t) = v_0t + \frac{at^2}{2}$. Подставим наши значения:</p><p>$s = 0 \cdot t + \frac{2.5t^2}{2} \Rightarrow s = 1.25t^2$.</p><p><strong>Характер движения тела</strong></p><p>Поскольку начальная скорость равна нулю ($v_0 = 0$), а ускорение постоянно и положительно ($a = 2.5 \text{ м/с}^2$), движение является прямолинейным равноускоренным из состояния покоя.</p><p>Заполненная таблица:</p><div class="table-wrap"><table border="1" style="border: 1px solid rgb(0, 0, 0);"><thead><tr><th style="border: 1px solid rgb(0, 0, 0);">Начальная скорость $v_0$, м/с</th><th style="border: 1px solid rgb(0, 0, 0);">Ускорение $\text{a}$, м/с²</th><th style="border: 1px solid rgb(0, 0, 0);">Уравнение скорости</th><th style="border: 1px solid rgb(0, 0, 0);">Уравнение перемещения</th><th style="border: 1px solid rgb(0, 0, 0);">Характер движения тела</th></tr></thead><tbody><tr><td style="border: 1px solid rgb(0, 0, 0);">0</td><td style="border: 1px solid rgb(0, 0, 0);">2.5</td><td style="border: 1px solid rgb(0, 0, 0);">$v = 2.5t$</td><td style="border: 1px solid rgb(0, 0, 0);">$s = 1.25t^2$</td><td style="border: 1px solid rgb(0, 0, 0);">Прямолинейное равноускоренное движение из состояния покоя</td></tr></tbody></table></div><p><strong>Ответ:</strong> Значения для таблицы: начальная скорость $v_0 = 0$ м/с; ускорение $a = 2.5$ м/с²; уравнение скорости $v = 2.5t$; уравнение перемещения $s = 1.25t^2$; характер движения – прямолинейное равноускоренное движение из состояния покоя.</p><p><strong>2.</strong> <strong>Дано:</strong></p><p>Уравнение движения тела: $x = -2 + t + 2t^2$ (м).</p><p>Все величины даны в системе СИ.</p><p><strong>Найти:</strong></p><p>$x_0, v_0, a$, уравнение скорости, уравнение перемещения, характер движения; построить график скорости $v(t)$.</p><p><strong>Решение:</strong></p><p>Общий вид уравнения для равноускоренного прямолинейного движения: $x(t) = x_0 + v_0t + \frac{at^2}{2}$. Сравним это уравнение с данным в условии: $x = -2 + 1 \cdot t + 2t^2$.</p><p><strong>Начальная координата $x_0$, м</strong></p><p>Из сравнения уравнений следует, что начальная координата $x_0 = -2$ м.</p><p><strong>Начальная скорость $v_0$, м/с</strong></p><p>Коэффициент при $\text{t}$ соответствует начальной скорости, следовательно $v_0 = 1$ м/с.</p><p><strong>Ускорение $\text{a}$, м/с²</strong></p><p>Коэффициент при $t^2$ равен $\frac{a}{2}$. В данном уравнении он равен 2. Отсюда: $\frac{a}{2} = 2 \Rightarrow a = 4 \text{ м/с}^2$.</p><p><strong>Уравнение скорости</strong></p><p>Общая формула для скорости: $v(t) = v_0 + at$. Подставим найденные значения $v_0$ и $\text{a}$: $v = 1 + 4t$.</p><p><strong>Уравнение перемещения</strong></p><p>Общая формула для перемещения: $s(t) = v_0t + \frac{at^2}{2}$. Подставим наши значения: $s = 1 \cdot t + \frac{4t^2}{2} \Rightarrow s = t + 2t^2$.</p><p><strong>Характер движения тела</strong></p><p>Поскольку ускорение постоянно и положительно ($a = 4 \text{ м/с}^2$), движение является прямолинейным равноускоренным.</p><p>Заполненная таблица:</p><div class="table-wrap"><table border="1" style="border: 1px solid rgb(0, 0, 0);"><thead><tr><th style="border: 1px solid rgb(0, 0, 0);">Начальная координата $x_0$, м</th><th style="border: 1px solid rgb(0, 0, 0);">Начальная скорость $v_0$, м/с</th><th style="border: 1px solid rgb(0, 0, 0);">Ускорение $\text{a}$, м/с²</th><th style="border: 1px solid rgb(0, 0, 0);">Уравнение скорости</th><th style="border: 1px solid rgb(0, 0, 0);">Уравнение перемещения</th><th style="border: 1px solid rgb(0, 0, 0);">Характер движения тела</th></tr></thead><tbody><tr><td style="border: 1px solid rgb(0, 0, 0);">-2</td><td style="border: 1px solid rgb(0, 0, 0);">1</td><td style="border: 1px solid rgb(0, 0, 0);">4</td><td style="border: 1px solid rgb(0, 0, 0);">$v = 1 + 4t$</td><td style="border: 1px solid rgb(0, 0, 0);">$s = t + 2t^2$</td><td style="border: 1px solid rgb(0, 0, 0);">Прямолинейное равноускоренное движение</td></tr></tbody></table></div><p><strong>Построение графика скорости движения тела</strong></p><p>График зависимости скорости от времени $v(t)$ описывается уравнением $v = 1 + 4t$. Это линейная функция, её график — прямая линия. Для построения достаточно двух точек:</p><p>При $t=0$, $v = 1 + 4 \cdot 0 = 1$ м/с. Координаты первой точки (0; 1).</p><p>При $t=2$, $v = 1 + 4 \cdot 2 = 9$ м/с. Координаты второй точки (2; 9).</p><p>Для построения графика на координатной плоскости с осями $\text{t}$ (с) и $\text{v}$ (м/с) нужно отметить эти две точки и провести через них прямую линию.</p><p><strong>Ответ:</strong></p><p>Результаты расчетов сведены в таблицу: $x_0 = -2$ м, $v_0 = 1$ м/с, $a = 4$ м/с², уравнение скорости $v = 1 + 4t$, уравнение перемещения $s = t + 2t^2$, характер движения – прямолинейное равноускоренное. График скорости $v(t)$ — прямая линия, проходящая через точки (0 с; 1 м/с) и (2 с; 9 м/с).</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1428620" "type" => "task" ] "previous" => array:2 [ "refs" => "1428618" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1089 #items: array:1 [ 0 => App\Models\Book {#1033} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1113 #items: array:1 [ 0 => App\Models\BookPage {#1112 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 1428960 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "69" "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/page-69" "field_display_title" => "69" "field_folder" => "1" "field_image_name" => "69" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1114 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1148 #items: array:1 [ 0 => App\Models\Book {#1115 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 894 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1117 #items: array:1 [ 0 => App\Models\Term {#1116 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ …10] #original: array:10 [ …10] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1118 #items: array:1 [ 0 => App\Models\Term {#1119 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1120 #items: array:1 [ 0 => App\Models\Term {#1121 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1122 #items: array:2 [ 0 => App\Models\Term {#1123 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 1 => App\Models\Term {#1124 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1125 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1126 #items: array:1 [ 0 => App\Models\Term {#1127 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ …10] #original: array:10 [ …10] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1128 #items: array:1 [ 0 => App\Models\Term {#1129 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1130 #items: array:1 [ 0 => App\Models\Term {#1131 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1132 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1133 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1134 #items: array:1 [ 0 => App\Models\Term {#1135 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] …2 } ] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1136 #items: array:1 [ 0 => App\Models\Term {#1137 …30} ] #escapeWhenCastingToString: false } "field_publication_number" => "3" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1138 #items: array:1 [ 0 => App\Models\Term {#1139 …30} ] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1140 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "изображена башня" "field_publication_year" => "2022" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "674" "field_priority" => null "field_default_folder" => "/fizika_09/maron-dm/" "field_isbn" => "978-5-09-111414-0" "field_cover" => array:1 [ 0 => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880" "alt" => "" "width" => "1888" "height" => "2427" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1141 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1142 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1143 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1144 #items: array:1 [ 0 => App\Models\Term {#1145 …30} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 556 "class_subject" => 493 ] ] #original: array:50 [ "id" => 894 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1117} "field_class" => Illuminate\Database\Eloquent\Collection {#1118} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1120} "field_author" => Illuminate\Database\Eloquent\Collection {#1122} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1125} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1126} "field_country" => Illuminate\Database\Eloquent\Collection {#1128} "field_city" => Illuminate\Database\Eloquent\Collection {#1130} "field_series" => Illuminate\Database\Eloquent\Collection {#1132} "field_umk" => Illuminate\Database\Eloquent\Collection {#1133} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1134} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1136} "field_publication_number" => "3" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1138} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1140} "field_under_the_edition_degree" => null "field_cover_description" => "изображена башня" "field_publication_year" => "2022" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "674" "field_priority" => null "field_default_folder" => "/fizika_09/maron-dm/" "field_isbn" => "978-5-09-111414-0" "field_cover" => array:1 [ 0 => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880" "alt" => "" "width" => "1888" "height" => "2427" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1141} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1142} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1143} "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1144} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 556 "class_subject" => 493 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1146 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1157 #items: array:1 [ 0 => App\Models\Element {#1156 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1683627 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1166 #items: array:1 [ 0 => App\Models\Edition {#1158 …30} ] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1428960" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "69-1.jpg" "alt" => null "width" => "1577" "height" => 2519 "path" => "/media/fizika_09/maron-dm/0-1/69-1.webp?ts=1758964756" ] ] ] #original: array:6 [ "id" => 1683627 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1166} "book_page" => array:2 [ "refs" => "1428960" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "69-1.jpg" "alt" => null "width" => "1577" "height" => 2519 "path" => "/media/fizika_09/maron-dm/0-1/69-1.webp?ts=1758964756" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1428961" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1428959" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1419 #items: array:3 [ 0 => App\Models\Task {#1149 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1428619 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "69" "field_page_end" => null "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp05-10" "field_display_title" => "Вариант 10" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1147 #items: [] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1150 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1153 #items: array:1 [ 0 => App\Models\Branch {#1151 …30} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1197 #items: array:2 [ 0 => App\Models\Branch {#1198 …30} 1 => App\Models\Branch {#1202 …30} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1206 #items: array:2 [ 0 => App\Models\Element {#1207 …30} 1 => App\Models\Element {#1215 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1428620" "type" => "task" ] "previous" => array:2 [ "refs" => "1428618" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1223 #items: array:1 [ 0 => App\Models\Book {#1164 …30} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1428960" "type" => "book_page" ] ] #original: array:24 [ "id" => 1428619 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "69" "field_page_end" => null "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp05-10" "field_display_title" => "Вариант 10" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1147} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1150} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1153} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1197} "content" => Illuminate\Database\Eloquent\Collection {#1206} "next" => array:2 [ "refs" => "1428620" "type" => "task" ] "previous" => array:2 [ "refs" => "1428618" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1223} "page" => array:2 [ "refs" => "1428960" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Task {#1224 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1428620 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "69" "field_page_end" => null "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp06-1" "field_display_title" => "Вариант 1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1225 #items: [] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1226 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1227 #items: array:1 [ 0 => App\Models\Branch {#1228 …30} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1263 #items: array:2 [ 0 => App\Models\Branch {#1228 …30} 1 => App\Models\Branch {#1264 …30} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1303 #items: array:2 [ 0 => App\Models\Element {#1304 …30} 1 => App\Models\Element {#1312 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1428621" "type" => "task" ] "previous" => array:2 [ "refs" => "1428619" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1320 #items: array:1 [ 0 => App\Models\Book {#1231 …30} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1428960" "type" => "book_page" ] ] #original: array:24 [ "id" => 1428620 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "69" "field_page_end" => null "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp06-1" "field_display_title" => "Вариант 1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1225} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1226} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1227} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1263} "content" => Illuminate\Database\Eloquent\Collection {#1303} "next" => array:2 [ "refs" => "1428621" "type" => "task" ] "previous" => array:2 [ "refs" => "1428619" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1320} "page" => array:2 [ "refs" => "1428960" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Task {#1321 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1428621 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "69" "field_page_end" => "70" "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp06-2" "field_display_title" => "Вариант 2" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1322 #items: [] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1323 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1324 #items: array:1 [ 0 => App\Models\Branch {#1325 …30} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1360 #items: array:2 [ 0 => App\Models\Branch {#1325 …30} 1 => App\Models\Branch {#1361 …30} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1400 #items: array:2 [ 0 => App\Models\Element {#1401 …30} 1 => App\Models\Element {#1409 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1428622" "type" => "task" ] "previous" => array:2 [ "refs" => "1428620" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1417 #items: array:1 [ 0 => App\Models\Book {#1328 …30} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1428960" "type" => "book_page" ] ] #original: array:24 [ "id" => 1428621 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "69" "field_page_end" => "70" "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp06-2" "field_display_title" => "Вариант 2" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1322} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1323} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1324} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1360} "content" => Illuminate\Database\Eloquent\Collection {#1400} "next" => array:2 [ "refs" => "1428622" "type" => "task" ] "previous" => array:2 [ "refs" => "1428620" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1417} "page" => array:2 [ "refs" => "1428960" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1428960 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "69" "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/page-69" "field_display_title" => "69" "field_folder" => "1" "field_image_name" => "69" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1114} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1148} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1146} "content" => Illuminate\Database\Eloquent\Collection {#1157} "next" => array:2 [ "refs" => "1428961" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1428959" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1419} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1428619 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "69" "field_page_end" => null "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp05-10" "field_display_title" => "Вариант 10" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#331} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1029} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1026} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1063} "content" => Illuminate\Database\Eloquent\Collection {#1072} "next" => array:2 [ "refs" => "1428620" "type" => "task" ] "previous" => array:2 [ "refs" => "1428618" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1089} "page" => array:2 [ "refs" => "1428960" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
Вариант 10 (с. 69)
Условие. Вариант 10 (с. 69)
скриншот условия
1. Заполните таблицу, используя график скорости движения тела (рис. 112).
$v, м/с$
Начальная скорость $v_0$, м/с
Ускорение $\text{a}$, м/$с^2$
Уравнение скорости
Уравнение перемещения
Характер движения тела
$t, с$
Рис. 112
2. Дано уравнение движения тела: $x = -2 + t + 2t^2$ (м). Заполните таблицу и постройте график скорости движения тела.
Начальная координата $x_0$, М
Начальная скорость $v_0$, м/с
Ускорение $\text{a}$, м/$с^2$
Уравнение скорости
Уравнение перемещения
Характер движения тела
Решение. Вариант 10 (с. 69)
1. Для заполнения таблицы необходимо проанализировать представленный график зависимости скорости от времени $v(t)$.
Начальная скорость $v_0$, м/с
Начальная скорость – это значение скорости в момент времени $t = 0$. Из графика видно, что линия зависимости скорости от времени проходит через начало координат, следовательно, начальная скорость тела $v_0 = 0$ м/с.
Ускорение $\text{a}$, м/с²
График скорости является прямой линией, что свидетельствует о равноускоренном движении. Ускорение $\text{a}$ постоянно и может быть найдено как тангенс угла наклона графика к оси времени. Для этого выберем на графике произвольную точку, например, с координатами $t = 4$ с и $v = 10$ м/с.
$a = \frac{\Delta v}{\Delta t} = \frac{v - v_0}{t - 0} = \frac{10 \text{ м/с} - 0 \text{ м/с}}{4 \text{ с}} = 2.5 \text{ м/с}^2$.
Уравнение скорости
Общий вид уравнения скорости для равноускоренного движения: $v(t) = v_0 + at$. Подставим найденные значения $v_0$ и $\text{a}$:
$v = 0 + 2.5t \Rightarrow v = 2.5t$.
Уравнение перемещения
Общий вид уравнения перемещения для равноускоренного движения: $s(t) = v_0t + \frac{at^2}{2}$. Подставим наши значения:
$s = 0 \cdot t + \frac{2.5t^2}{2} \Rightarrow s = 1.25t^2$.
Характер движения тела
Поскольку начальная скорость равна нулю ($v_0 = 0$), а ускорение постоянно и положительно ($a = 2.5 \text{ м/с}^2$), движение является прямолинейным равноускоренным из состояния покоя.
Заполненная таблица:
| Начальная скорость $v_0$, м/с | Ускорение $\text{a}$, м/с² | Уравнение скорости | Уравнение перемещения | Характер движения тела |
|---|---|---|---|---|
| 0 | 2.5 | $v = 2.5t$ | $s = 1.25t^2$ | Прямолинейное равноускоренное движение из состояния покоя |
Ответ: Значения для таблицы: начальная скорость $v_0 = 0$ м/с; ускорение $a = 2.5$ м/с²; уравнение скорости $v = 2.5t$; уравнение перемещения $s = 1.25t^2$; характер движения – прямолинейное равноускоренное движение из состояния покоя.
2. Дано:
Уравнение движения тела: $x = -2 + t + 2t^2$ (м).
Все величины даны в системе СИ.
Найти:
$x_0, v_0, a$, уравнение скорости, уравнение перемещения, характер движения; построить график скорости $v(t)$.
Решение:
Общий вид уравнения для равноускоренного прямолинейного движения: $x(t) = x_0 + v_0t + \frac{at^2}{2}$. Сравним это уравнение с данным в условии: $x = -2 + 1 \cdot t + 2t^2$.
Начальная координата $x_0$, м
Из сравнения уравнений следует, что начальная координата $x_0 = -2$ м.
Начальная скорость $v_0$, м/с
Коэффициент при $\text{t}$ соответствует начальной скорости, следовательно $v_0 = 1$ м/с.
Ускорение $\text{a}$, м/с²
Коэффициент при $t^2$ равен $\frac{a}{2}$. В данном уравнении он равен 2. Отсюда: $\frac{a}{2} = 2 \Rightarrow a = 4 \text{ м/с}^2$.
Уравнение скорости
Общая формула для скорости: $v(t) = v_0 + at$. Подставим найденные значения $v_0$ и $\text{a}$: $v = 1 + 4t$.
Уравнение перемещения
Общая формула для перемещения: $s(t) = v_0t + \frac{at^2}{2}$. Подставим наши значения: $s = 1 \cdot t + \frac{4t^2}{2} \Rightarrow s = t + 2t^2$.
Характер движения тела
Поскольку ускорение постоянно и положительно ($a = 4 \text{ м/с}^2$), движение является прямолинейным равноускоренным.
Заполненная таблица:
| Начальная координата $x_0$, м | Начальная скорость $v_0$, м/с | Ускорение $\text{a}$, м/с² | Уравнение скорости | Уравнение перемещения | Характер движения тела |
|---|---|---|---|---|---|
| -2 | 1 | 4 | $v = 1 + 4t$ | $s = t + 2t^2$ | Прямолинейное равноускоренное движение |
Построение графика скорости движения тела
График зависимости скорости от времени $v(t)$ описывается уравнением $v = 1 + 4t$. Это линейная функция, её график — прямая линия. Для построения достаточно двух точек:
При $t=0$, $v = 1 + 4 \cdot 0 = 1$ м/с. Координаты первой точки (0; 1).
При $t=2$, $v = 1 + 4 \cdot 2 = 9$ м/с. Координаты второй точки (2; 9).
Для построения графика на координатной плоскости с осями $\text{t}$ (с) и $\text{v}$ (м/с) нужно отметить эти две точки и провести через них прямую линию.
Ответ:
Результаты расчетов сведены в таблицу: $x_0 = -2$ м, $v_0 = 1$ м/с, $a = 4$ м/с², уравнение скорости $v = 1 + 4t$, уравнение перемещения $s = t + 2t^2$, характер движения – прямолинейное равноускоренное. График скорости $v(t)$ — прямая линия, проходящая через точки (0 с; 1 м/с) и (2 с; 9 м/с).
Другие задания:
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