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Вариант 2, страница 59 - 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-3. Прямолинейное равномерное движение. Графические задачи - страница 59.
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" => 1428591 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "59" "field_page_end" => null "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp03-2" "field_display_title" => "Вариант 2" "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 {#342} 1 => 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" => 1428177 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "СР-3. Прямолинейное равномерное движение. Графические задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1065 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "59" "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: array:1 [ 0 => 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" => 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 {#1069 #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 {#1070 #items: array:1 [ 0 => App\Models\Book {#1033} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1071 #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 {#1069} "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 {#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 } ] #original: array:24 [ "id" => 1428177 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "СР-3. Прямолинейное равномерное движение. Графические задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1065} "field_page_start" => "59" "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 => "*" ] } ] #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" => 1682906 "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" => "1428591" "type" => "task" ] "text" => "<p><strong>1.</strong> Графики движения двух тел представлены на рисунке 94. Напишите уравнения движения $x = x(t)$ этих тел. Определите место и время их встречи графически и аналитически (с помощью уравнений движения).</p><p><strong>2.</strong> Даны уравнения движения двух тел: $x_1 = 4 + 2t$ (м) и $x_2 = 8 - 2t$ (м). Постройте графики движения этих тел и определите место и время их встречи графически и аналитически.</p><p>Рис. 94</p>" "img" => array:1 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "1413" "height" => 682 "path" => "/media/fizika_09/maron-dm/0-cp03/2-1.webp?ts=1758964211" ] ] ] #original: array:7 [ "id" => 1682906 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1074} "task" => array:2 [ "refs" => "1428591" "type" => "task" ] "text" => "<p><strong>1.</strong> Графики движения двух тел представлены на рисунке 94. Напишите уравнения движения $x = x(t)$ этих тел. Определите место и время их встречи графически и аналитически (с помощью уравнений движения).</p><p><strong>2.</strong> Даны уравнения движения двух тел: $x_1 = 4 + 2t$ (м) и $x_2 = 8 - 2t$ (м). Постройте графики движения этих тел и определите место и время их встречи графически и аналитически.</p><p>Рис. 94</p>" "img" => array:1 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "1413" "height" => 682 "path" => "/media/fizika_09/maron-dm/0-cp03/2-1.webp?ts=1758964211" ] ] ] #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" => 1730608 "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" => "1428591" "type" => "task" ] "text" => "<p><strong>1.</strong> <strong>Дано:</strong></p><p>График зависимости координаты от времени $x(t)$ для двух тел (Рис. 94). Все величины представлены в системе СИ.</p><p><strong>Найти:</strong></p><p><strong>1.</strong> Уравнения движения $x_1(t)$ и $x_2(t)$.</p><p><strong>2.</strong> Время $t_{встр}$ и место $x_{встр}$ встречи графически.</p><p><strong>3.</strong> Время $t_{встр}$ и место $x_{встр}$ встречи аналитически.</p><p><strong>Решение:</strong></p><p><em>а) Составление уравнений движения.</em></p><p>Так как графики зависимости координаты от времени являются прямыми линиями, движение тел является равномерным и прямолинейным. Уравнение такого движения в общем виде: $x(t) = x_0 + v_x t$, где $x_0$ — начальная координата (координата в момент времени $t=0$), а $v_x$ — проекция скорости на ось Ох.</p><p><u>Для первого тела (график 1):</u></p><p>Из графика определяем начальную координату: при $t=0$, $x_1 = 0$ м. Значит, $x_{01} = 0$ м.</p><p>Для определения скорости $v_{1x}$ выберем на графике точку, например, с координатами $t = 4$ с и $x = 4$ м. Скорость равна тангенсу угла наклона графика:</p><p>$v_{1x} = \frac{\Delta x}{\Delta t} = \frac{4 \text{ м} - 0 \text{ м}}{4 \text{ с} - 0 \text{ с}} = 1 \text{ м/с}$.</p><p>Подставляем найденные значения в общую формулу. Уравнение движения первого тела: $x_1(t) = 0 + 1 \cdot t$, или $x_1(t) = t$.</p><p><u>Для второго тела (график 2):</u></p><p>Из графика определяем начальную координату: при $t=0$, $x_2 = 4$ м. Значит, $x_{02} = 4$ м.</p><p>Для определения скорости $v_{2x}$ выберем на графике точку, например, с координатами $t = 4$ с и $x = 0$ м.</p><p>$v_{2x} = \frac{\Delta x}{\Delta t} = \frac{0 \text{ м} - 4 \text{ м}}{4 \text{ с} - 0 \text{ с}} = -1 \text{ м/с}$.</p><p>Подставляем найденные значения в общую формулу. Уравнение движения второго тела: $x_2(t) = 4 - 1 \cdot t$, или $x_2(t) = 4 - t$.</p><p><em>б) Определение места и времени встречи графически.</em></p><p>Встреча тел происходит в тот момент времени, когда их координаты равны. На графике это соответствует точке пересечения линий. По графику видно, что точка пересечения имеет координаты $t = 2$ с и $x = 2$ м.</p><p><em>в) Определение места и времени встречи аналитически.</em></p><p>В момент встречи $t_{встр}$ координаты тел должны быть одинаковы: $x_1(t_{встр}) = x_2(t_{встр})$. Приравняем полученные уравнения:</p><p>$t_{встр} = 4 - t_{встр}$</p><p>$2t_{встр} = 4$</p><p>$t_{встр} = 2$ с.</p><p>Чтобы найти координату встречи $x_{встр}$, подставим найденное время в любое из уравнений движения:</p><p>$x_{встр} = x_1(2) = 2$ м.</p><p>Проверим с помощью второго уравнения: $x_{встр} = x_2(2) = 4 - 2 = 2$ м.</p><p>Аналитический расчет подтверждает данные, полученные из графика.</p><p><strong>Ответ:</strong> Уравнения движения тел: $x_1(t) = t$ и $x_2(t) = 4 - t$. Тела встретятся в момент времени $t = 2$ с в точке с координатой $x = 2$ м.</p><p><strong>2.</strong> <strong>Дано:</strong></p><p>Уравнение движения первого тела: $x_1 = 4 + 2t$ (м).</p><p>Уравнение движения второго тела: $x_2 = 8 - 2t$ (м).</p><p>Все величины представлены в системе СИ.</p><p><strong>Найти:</strong></p><p><strong>1.</strong> Построить графики движения $x_1(t)$ и $x_2(t)$.</p><p><strong>2.</strong> Время $t_{встр}$ и место $x_{встр}$ встречи графически.</p><p><strong>3.</strong> Время $t_{встр}$ и место $x_{встр}$ встречи аналитически.</p><p><strong>Решение:</strong></p><p><em>а) Аналитическое определение места и времени встречи.</em></p><p>В момент встречи координаты тел равны: $x_1(t_{встр}) = x_2(t_{встр})$.</p><p>Приравняем правые части данных уравнений:</p><p>$4 + 2t_{встр} = 8 - 2t_{встр}$</p><p>Решим это уравнение относительно $t_{встр}$:</p><p>$2t_{встр} + 2t_{встр} = 8 - 4$</p><p>$4t_{встр} = 4$</p><p>$t_{встр} = 1$ с.</p><p>Теперь найдем координату встречи $x_{встр}$, подставив $t_{встр} = 1$ с в любое из уравнений:</p><p>$x_{встр} = x_1(1) = 4 + 2 \cdot 1 = 6$ м.</p><p>Проверка по второму уравнению: $x_{встр} = x_2(1) = 8 - 2 \cdot 1 = 6$ м.</p><p>Итак, аналитически найдено, что встреча произойдет через 1 с в точке с координатой 6 м.</p><p><em>б) Построение графиков и графическое определение места и времени встречи.</em></p><p>Оба уравнения вида $x = x_0 + v_x t$ описывают равномерное прямолинейное движение, их графики — прямые линии. Для построения каждой прямой найдем координаты двух точек.</p><p><u>Для первого тела ($x_1 = 4 + 2t$):</u></p><p><strong>1.</strong> При $t = 0$ с, $x_1 = 4 + 2 \cdot 0 = 4$ м. Точка (0; 4).</p><p><strong>2.</strong> При $t = 2$ с, $x_1 = 4 + 2 \cdot 2 = 8$ м. Точка (2; 8).</p><p><u>Для второго тела ($x_2 = 8 - 2t$):</u></p><p><strong>1.</strong> При $t = 0$ с, $x_2 = 8 - 2 \cdot 0 = 8$ м. Точка (0; 8).</p><p><strong>2.</strong> При $t = 2$ с, $x_2 = 8 - 2 \cdot 2 = 4$ м. Точка (2; 4).</p><p>Построим систему координат, отложив по горизонтальной оси время $\text{t}$ в секундах, а по вертикальной — координату $\text{x}$ в метрах. Нанесем вычисленные точки для каждого тела и проведем через них прямые. Точка пересечения этих двух прямых на графике и будет соответствовать моменту и месту встречи тел. При точном построении графики пересекутся в точке с координатами $(1; 6)$.</p><p>Таким образом, графический метод дает тот же результат: время встречи $t_{встр} = 1$ с, место встречи $x_{встр} = 6$ м.</p><p><strong>Ответ:</strong> Тела встретятся в момент времени $t = 1$ с в точке с координатой $x = 6$ м. Графики движения представляют собой две прямые, пересекающиеся в точке с координатами (1; 6).</p>" ] #original: array:6 [ "id" => 1730608 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1082} "task" => array:2 [ "refs" => "1428591" "type" => "task" ] "text" => "<p><strong>1.</strong> <strong>Дано:</strong></p><p>График зависимости координаты от времени $x(t)$ для двух тел (Рис. 94). Все величины представлены в системе СИ.</p><p><strong>Найти:</strong></p><p><strong>1.</strong> Уравнения движения $x_1(t)$ и $x_2(t)$.</p><p><strong>2.</strong> Время $t_{встр}$ и место $x_{встр}$ встречи графически.</p><p><strong>3.</strong> Время $t_{встр}$ и место $x_{встр}$ встречи аналитически.</p><p><strong>Решение:</strong></p><p><em>а) Составление уравнений движения.</em></p><p>Так как графики зависимости координаты от времени являются прямыми линиями, движение тел является равномерным и прямолинейным. Уравнение такого движения в общем виде: $x(t) = x_0 + v_x t$, где $x_0$ — начальная координата (координата в момент времени $t=0$), а $v_x$ — проекция скорости на ось Ох.</p><p><u>Для первого тела (график 1):</u></p><p>Из графика определяем начальную координату: при $t=0$, $x_1 = 0$ м. Значит, $x_{01} = 0$ м.</p><p>Для определения скорости $v_{1x}$ выберем на графике точку, например, с координатами $t = 4$ с и $x = 4$ м. Скорость равна тангенсу угла наклона графика:</p><p>$v_{1x} = \frac{\Delta x}{\Delta t} = \frac{4 \text{ м} - 0 \text{ м}}{4 \text{ с} - 0 \text{ с}} = 1 \text{ м/с}$.</p><p>Подставляем найденные значения в общую формулу. Уравнение движения первого тела: $x_1(t) = 0 + 1 \cdot t$, или $x_1(t) = t$.</p><p><u>Для второго тела (график 2):</u></p><p>Из графика определяем начальную координату: при $t=0$, $x_2 = 4$ м. Значит, $x_{02} = 4$ м.</p><p>Для определения скорости $v_{2x}$ выберем на графике точку, например, с координатами $t = 4$ с и $x = 0$ м.</p><p>$v_{2x} = \frac{\Delta x}{\Delta t} = \frac{0 \text{ м} - 4 \text{ м}}{4 \text{ с} - 0 \text{ с}} = -1 \text{ м/с}$.</p><p>Подставляем найденные значения в общую формулу. Уравнение движения второго тела: $x_2(t) = 4 - 1 \cdot t$, или $x_2(t) = 4 - t$.</p><p><em>б) Определение места и времени встречи графически.</em></p><p>Встреча тел происходит в тот момент времени, когда их координаты равны. На графике это соответствует точке пересечения линий. По графику видно, что точка пересечения имеет координаты $t = 2$ с и $x = 2$ м.</p><p><em>в) Определение места и времени встречи аналитически.</em></p><p>В момент встречи $t_{встр}$ координаты тел должны быть одинаковы: $x_1(t_{встр}) = x_2(t_{встр})$. Приравняем полученные уравнения:</p><p>$t_{встр} = 4 - t_{встр}$</p><p>$2t_{встр} = 4$</p><p>$t_{встр} = 2$ с.</p><p>Чтобы найти координату встречи $x_{встр}$, подставим найденное время в любое из уравнений движения:</p><p>$x_{встр} = x_1(2) = 2$ м.</p><p>Проверим с помощью второго уравнения: $x_{встр} = x_2(2) = 4 - 2 = 2$ м.</p><p>Аналитический расчет подтверждает данные, полученные из графика.</p><p><strong>Ответ:</strong> Уравнения движения тел: $x_1(t) = t$ и $x_2(t) = 4 - t$. Тела встретятся в момент времени $t = 2$ с в точке с координатой $x = 2$ м.</p><p><strong>2.</strong> <strong>Дано:</strong></p><p>Уравнение движения первого тела: $x_1 = 4 + 2t$ (м).</p><p>Уравнение движения второго тела: $x_2 = 8 - 2t$ (м).</p><p>Все величины представлены в системе СИ.</p><p><strong>Найти:</strong></p><p><strong>1.</strong> Построить графики движения $x_1(t)$ и $x_2(t)$.</p><p><strong>2.</strong> Время $t_{встр}$ и место $x_{встр}$ встречи графически.</p><p><strong>3.</strong> Время $t_{встр}$ и место $x_{встр}$ встречи аналитически.</p><p><strong>Решение:</strong></p><p><em>а) Аналитическое определение места и времени встречи.</em></p><p>В момент встречи координаты тел равны: $x_1(t_{встр}) = x_2(t_{встр})$.</p><p>Приравняем правые части данных уравнений:</p><p>$4 + 2t_{встр} = 8 - 2t_{встр}$</p><p>Решим это уравнение относительно $t_{встр}$:</p><p>$2t_{встр} + 2t_{встр} = 8 - 4$</p><p>$4t_{встр} = 4$</p><p>$t_{встр} = 1$ с.</p><p>Теперь найдем координату встречи $x_{встр}$, подставив $t_{встр} = 1$ с в любое из уравнений:</p><p>$x_{встр} = x_1(1) = 4 + 2 \cdot 1 = 6$ м.</p><p>Проверка по второму уравнению: $x_{встр} = x_2(1) = 8 - 2 \cdot 1 = 6$ м.</p><p>Итак, аналитически найдено, что встреча произойдет через 1 с в точке с координатой 6 м.</p><p><em>б) Построение графиков и графическое определение места и времени встречи.</em></p><p>Оба уравнения вида $x = x_0 + v_x t$ описывают равномерное прямолинейное движение, их графики — прямые линии. Для построения каждой прямой найдем координаты двух точек.</p><p><u>Для первого тела ($x_1 = 4 + 2t$):</u></p><p><strong>1.</strong> При $t = 0$ с, $x_1 = 4 + 2 \cdot 0 = 4$ м. Точка (0; 4).</p><p><strong>2.</strong> При $t = 2$ с, $x_1 = 4 + 2 \cdot 2 = 8$ м. Точка (2; 8).</p><p><u>Для второго тела ($x_2 = 8 - 2t$):</u></p><p><strong>1.</strong> При $t = 0$ с, $x_2 = 8 - 2 \cdot 0 = 8$ м. Точка (0; 8).</p><p><strong>2.</strong> При $t = 2$ с, $x_2 = 8 - 2 \cdot 2 = 4$ м. Точка (2; 4).</p><p>Построим систему координат, отложив по горизонтальной оси время $\text{t}$ в секундах, а по вертикальной — координату $\text{x}$ в метрах. Нанесем вычисленные точки для каждого тела и проведем через них прямые. Точка пересечения этих двух прямых на графике и будет соответствовать моменту и месту встречи тел. При точном построении графики пересекутся в точке с координатами $(1; 6)$.</p><p>Таким образом, графический метод дает тот же результат: время встречи $t_{встр} = 1$ с, место встречи $x_{встр} = 6$ м.</p><p><strong>Ответ:</strong> Тела встретятся в момент времени $t = 1$ с в точке с координатой $x = 6$ м. Графики движения представляют собой две прямые, пересекающиеся в точке с координатами (1; 6).</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" => "1428592" "type" => "task" ] "previous" => array:2 [ "refs" => "1428590" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1089 #items: array:1 [ 0 => App\Models\Book {#1033} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1202 #items: array:1 [ 0 => App\Models\BookPage {#1100 #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" => 1428950 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "59" "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/page-59" "field_display_title" => "59" "field_folder" => "1" "field_image_name" => "59" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1106 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1105 #items: array:1 [ 0 => App\Models\Book {#1107 #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 {#1108 #items: array:1 [ 0 => App\Models\Term {#1109 #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 {#1110 #items: array:1 [ 0 => App\Models\Term {#1111 #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 {#1112 #items: array:1 [ 0 => App\Models\Term {#1113 #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 {#1114 #items: array:2 [ 0 => App\Models\Term {#1115 #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 {#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: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 {#1117 #items: [] #escapeWhenCastingToString: false } "field_book_type" => 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: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 {#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_city" => Illuminate\Database\Eloquent\Collection {#1122 #items: array:1 [ 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: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 {#1124 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1125 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => 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: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 {#1128 #items: array:1 [ 0 => App\Models\Term {#1129 …30} ] #escapeWhenCastingToString: false } "field_publication_number" => "3" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1130 #items: array:1 [ 0 => App\Models\Term {#1131 …30} ] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1132 #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 {#1133 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1134 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1135 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1136 #items: array:1 [ 0 => App\Models\Term {#1137 …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 {#1108} "field_class" => Illuminate\Database\Eloquent\Collection {#1110} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1112} "field_author" => Illuminate\Database\Eloquent\Collection {#1114} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1117} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1118} "field_country" => Illuminate\Database\Eloquent\Collection {#1120} "field_city" => Illuminate\Database\Eloquent\Collection {#1122} "field_series" => Illuminate\Database\Eloquent\Collection {#1124} "field_umk" => Illuminate\Database\Eloquent\Collection {#1125} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1126} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1128} "field_publication_number" => "3" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1130} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1132} "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 {#1133} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1134} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1135} "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1136} "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 {#1138 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1139 #items: array:1 [ 0 => App\Models\Element {#1140 #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" => 1683617 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1141 #items: array:1 [ 0 => App\Models\Edition {#1142 …30} ] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1428950" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "59-1.jpg" "alt" => null "width" => "1588" "height" => 2526 "path" => "/media/fizika_09/maron-dm/0-1/59-1.webp?ts=1758964756" ] ] ] #original: array:6 [ "id" => 1683617 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1141} "book_page" => array:2 [ "refs" => "1428950" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "59-1.jpg" "alt" => null "width" => "1588" "height" => 2526 "path" => "/media/fizika_09/maron-dm/0-1/59-1.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" => "1428951" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1428949" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1148 #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" => 1428590 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "59" "field_page_end" => null "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp03-1" "field_display_title" => "Вариант 1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1150 #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 {#1151 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1152 #items: array:1 [ 0 => App\Models\Branch {#1153 …30} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1157 #items: array:2 [ 0 => App\Models\Branch {#1153 …30} 1 => App\Models\Branch {#1158 …30} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1166 #items: array:2 [ 0 => App\Models\Element {#1167 …30} 1 => App\Models\Element {#1169 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1428591" "type" => "task" ] "previous" => array:2 [ "refs" => "1428589" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1177 #items: array:1 [ 0 => App\Models\Book {#1107} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1428950" "type" => "book_page" ] ] #original: array:24 [ "id" => 1428590 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "59" "field_page_end" => null "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp03-1" "field_display_title" => "Вариант 1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1150} "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 {#1151} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1152} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1157} "content" => Illuminate\Database\Eloquent\Collection {#1166} "next" => array:2 [ "refs" => "1428591" "type" => "task" ] "previous" => array:2 [ "refs" => "1428589" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1177} "page" => array:2 [ "refs" => "1428950" "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 {#1178 #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" => 1428591 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "59" "field_page_end" => null "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp03-2" "field_display_title" => "Вариант 2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1179 #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 {#1180 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1181 #items: array:1 [ 0 => App\Models\Branch {#1153 …30} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1182 #items: array:2 [ 0 => App\Models\Branch {#1153 …30} 1 => App\Models\Branch {#1158 …30} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1183 #items: array:2 [ 0 => App\Models\Element {#1184 …30} 1 => App\Models\Element {#1186 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1428592" "type" => "task" ] "previous" => array:2 [ "refs" => "1428590" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1188 #items: array:1 [ 0 => App\Models\Book {#1107} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1428950" "type" => "book_page" ] ] #original: array:24 [ "id" => 1428591 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "59" "field_page_end" => null "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp03-2" "field_display_title" => "Вариант 2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1179} "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 {#1180} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1181} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1182} "content" => Illuminate\Database\Eloquent\Collection {#1183} "next" => array:2 [ "refs" => "1428592" "type" => "task" ] "previous" => array:2 [ "refs" => "1428590" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1188} "page" => array:2 [ "refs" => "1428950" "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 {#1189 #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" => 1428592 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "59" "field_page_end" => null "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp03-3" "field_display_title" => "Вариант 3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1190 #items: [] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null 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Вариант 2 (с. 59)
Условие. Вариант 2 (с. 59)
скриншот условия
1. Графики движения двух тел представлены на рисунке 94. Напишите уравнения движения $x = x(t)$ этих тел. Определите место и время их встречи графически и аналитически (с помощью уравнений движения).
2. Даны уравнения движения двух тел: $x_1 = 4 + 2t$ (м) и $x_2 = 8 - 2t$ (м). Постройте графики движения этих тел и определите место и время их встречи графически и аналитически.
Рис. 94
Решение. Вариант 2 (с. 59)
1. Дано:
График зависимости координаты от времени $x(t)$ для двух тел (Рис. 94). Все величины представлены в системе СИ.
Найти:
1. Уравнения движения $x_1(t)$ и $x_2(t)$.
2. Время $t_{встр}$ и место $x_{встр}$ встречи графически.
3. Время $t_{встр}$ и место $x_{встр}$ встречи аналитически.
Решение:
а) Составление уравнений движения.
Так как графики зависимости координаты от времени являются прямыми линиями, движение тел является равномерным и прямолинейным. Уравнение такого движения в общем виде: $x(t) = x_0 + v_x t$, где $x_0$ — начальная координата (координата в момент времени $t=0$), а $v_x$ — проекция скорости на ось Ох.
Для первого тела (график 1):
Из графика определяем начальную координату: при $t=0$, $x_1 = 0$ м. Значит, $x_{01} = 0$ м.
Для определения скорости $v_{1x}$ выберем на графике точку, например, с координатами $t = 4$ с и $x = 4$ м. Скорость равна тангенсу угла наклона графика:
$v_{1x} = \frac{\Delta x}{\Delta t} = \frac{4 \text{ м} - 0 \text{ м}}{4 \text{ с} - 0 \text{ с}} = 1 \text{ м/с}$.
Подставляем найденные значения в общую формулу. Уравнение движения первого тела: $x_1(t) = 0 + 1 \cdot t$, или $x_1(t) = t$.
Для второго тела (график 2):
Из графика определяем начальную координату: при $t=0$, $x_2 = 4$ м. Значит, $x_{02} = 4$ м.
Для определения скорости $v_{2x}$ выберем на графике точку, например, с координатами $t = 4$ с и $x = 0$ м.
$v_{2x} = \frac{\Delta x}{\Delta t} = \frac{0 \text{ м} - 4 \text{ м}}{4 \text{ с} - 0 \text{ с}} = -1 \text{ м/с}$.
Подставляем найденные значения в общую формулу. Уравнение движения второго тела: $x_2(t) = 4 - 1 \cdot t$, или $x_2(t) = 4 - t$.
б) Определение места и времени встречи графически.
Встреча тел происходит в тот момент времени, когда их координаты равны. На графике это соответствует точке пересечения линий. По графику видно, что точка пересечения имеет координаты $t = 2$ с и $x = 2$ м.
в) Определение места и времени встречи аналитически.
В момент встречи $t_{встр}$ координаты тел должны быть одинаковы: $x_1(t_{встр}) = x_2(t_{встр})$. Приравняем полученные уравнения:
$t_{встр} = 4 - t_{встр}$
$2t_{встр} = 4$
$t_{встр} = 2$ с.
Чтобы найти координату встречи $x_{встр}$, подставим найденное время в любое из уравнений движения:
$x_{встр} = x_1(2) = 2$ м.
Проверим с помощью второго уравнения: $x_{встр} = x_2(2) = 4 - 2 = 2$ м.
Аналитический расчет подтверждает данные, полученные из графика.
Ответ: Уравнения движения тел: $x_1(t) = t$ и $x_2(t) = 4 - t$. Тела встретятся в момент времени $t = 2$ с в точке с координатой $x = 2$ м.
2. Дано:
Уравнение движения первого тела: $x_1 = 4 + 2t$ (м).
Уравнение движения второго тела: $x_2 = 8 - 2t$ (м).
Все величины представлены в системе СИ.
Найти:
1. Построить графики движения $x_1(t)$ и $x_2(t)$.
2. Время $t_{встр}$ и место $x_{встр}$ встречи графически.
3. Время $t_{встр}$ и место $x_{встр}$ встречи аналитически.
Решение:
а) Аналитическое определение места и времени встречи.
В момент встречи координаты тел равны: $x_1(t_{встр}) = x_2(t_{встр})$.
Приравняем правые части данных уравнений:
$4 + 2t_{встр} = 8 - 2t_{встр}$
Решим это уравнение относительно $t_{встр}$:
$2t_{встр} + 2t_{встр} = 8 - 4$
$4t_{встр} = 4$
$t_{встр} = 1$ с.
Теперь найдем координату встречи $x_{встр}$, подставив $t_{встр} = 1$ с в любое из уравнений:
$x_{встр} = x_1(1) = 4 + 2 \cdot 1 = 6$ м.
Проверка по второму уравнению: $x_{встр} = x_2(1) = 8 - 2 \cdot 1 = 6$ м.
Итак, аналитически найдено, что встреча произойдет через 1 с в точке с координатой 6 м.
б) Построение графиков и графическое определение места и времени встречи.
Оба уравнения вида $x = x_0 + v_x t$ описывают равномерное прямолинейное движение, их графики — прямые линии. Для построения каждой прямой найдем координаты двух точек.
Для первого тела ($x_1 = 4 + 2t$):
1. При $t = 0$ с, $x_1 = 4 + 2 \cdot 0 = 4$ м. Точка (0; 4).
2. При $t = 2$ с, $x_1 = 4 + 2 \cdot 2 = 8$ м. Точка (2; 8).
Для второго тела ($x_2 = 8 - 2t$):
1. При $t = 0$ с, $x_2 = 8 - 2 \cdot 0 = 8$ м. Точка (0; 8).
2. При $t = 2$ с, $x_2 = 8 - 2 \cdot 2 = 4$ м. Точка (2; 4).
Построим систему координат, отложив по горизонтальной оси время $\text{t}$ в секундах, а по вертикальной — координату $\text{x}$ в метрах. Нанесем вычисленные точки для каждого тела и проведем через них прямые. Точка пересечения этих двух прямых на графике и будет соответствовать моменту и месту встречи тел. При точном построении графики пересекутся в точке с координатами $(1; 6)$.
Таким образом, графический метод дает тот же результат: время встречи $t_{встр} = 1$ с, место встречи $x_{встр} = 6$ м.
Ответ: Тела встретятся в момент времени $t = 1$ с в точке с координатой $x = 6$ м. Графики движения представляют собой две прямые, пересекающиеся в точке с координатами (1; 6).
Другие задания:
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