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Вариант 8, страница 68 - 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 68.
App\Models\Task {#1030 // 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" => 1428617 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "68" "field_page_end" => null "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp05-8" "field_display_title" => "Вариант 8" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1036 #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 {#1034 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1073 #items: array:1 [ 0 => App\Models\Branch {#1035 #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 {#1038 #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 {#1037 #items: array:1 [ 0 => App\Models\Book {#1039 #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 {#1040 #items: array:1 [ 0 => App\Models\Term {#1041 #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 {#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: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 {#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 [ …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 {#1046 #items: array:2 [ 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: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 {#1048 #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 {#1049 #items: [] #escapeWhenCastingToString: false } "field_book_type" => 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: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 {#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: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 {#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 [ …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 {#1056 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1057 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1058 #items: array:1 [ 0 => App\Models\Term {#1059 #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_standart_of_education" => 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: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_publication_number" => "3" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1062 #items: array:1 [ 0 => App\Models\Term {#1063 #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_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064 #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 {#1065 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1066 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1067 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1068 #items: array:1 [ 0 => App\Models\Term {#1069 #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_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 {#1040} "field_class" => Illuminate\Database\Eloquent\Collection {#1042} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1044} "field_author" => Illuminate\Database\Eloquent\Collection {#1046} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1049} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1050} "field_country" => Illuminate\Database\Eloquent\Collection {#1052} "field_city" => Illuminate\Database\Eloquent\Collection {#1054} "field_series" => Illuminate\Database\Eloquent\Collection {#1056} "field_umk" => Illuminate\Database\Eloquent\Collection {#1057} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1058} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1060} "field_publication_number" => "3" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1062} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064} "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 {#1065} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1066} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1067} "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1068} "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 {#1070 #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 {#1038} "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 {#1037} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1070} ] #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 {#1109 #items: array:2 [ 0 => App\Models\Branch {#1117 #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 {#1118 #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 {#1152 #items: array:1 [ 0 => App\Models\Book {#1119 #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 {#1121 #items: array:1 [ 0 => App\Models\Term {#1120 #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 {#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 [ "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 {#1124 #items: array:1 [ 0 => App\Models\Term {#1125 #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 {#1126 #items: array:2 [ 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: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 {#1128 #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 {#1129 #items: [] #escapeWhenCastingToString: false } "field_book_type" => 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: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 {#1132 #items: array:1 [ 0 => App\Models\Term {#1133 #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 {#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 [ "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 {#1136 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1137 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1138 #items: array:1 [ 0 => App\Models\Term {#1139 #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 {#1140 #items: array:1 [ 0 => App\Models\Term {#1141 #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 {#1142 #items: array:1 [ 0 => App\Models\Term {#1143 #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 {#1144 #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 {#1145 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1146 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1147 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1148 #items: array:1 [ 0 => App\Models\Term {#1149 #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 {#1121} "field_class" => Illuminate\Database\Eloquent\Collection {#1122} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1124} "field_author" => Illuminate\Database\Eloquent\Collection {#1126} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1129} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1130} "field_country" => Illuminate\Database\Eloquent\Collection {#1132} "field_city" => Illuminate\Database\Eloquent\Collection {#1134} "field_series" => Illuminate\Database\Eloquent\Collection {#1136} "field_umk" => Illuminate\Database\Eloquent\Collection {#1137} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1138} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1140} "field_publication_number" => "3" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1142} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1144} "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 {#1145} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1146} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1147} "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1148} "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 {#1150 #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 {#1118} "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 {#1152} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1150} ] #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 {#1151 #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 {#1153 #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 {#1154 #items: array:1 [ 0 => App\Models\Book {#1119} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1155 #items: array:1 [ 0 => App\Models\Branch {#1035} ] #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 {#1153} "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 {#1154} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1155} ] #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 {#1071 #items: array:2 [ 0 => App\Models\Element {#1100 #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" => 1682932 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1090 #items: array:1 [ 0 => App\Models\Edition {#1098 #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 {#1096 #items: array:1 [ 0 => App\Models\Term {#1099 #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 {#1097 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1094 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1095 #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 {#1096} "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 {#1097} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1094} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1095} "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" => "1428617" "type" => "task" ] "text" => "<p><strong>1.</strong> Заполните таблицу, используя график скорости движения тела (рис. 110).</p><p>Начальная скорость $v_0$, м/с<br>Ускорение $\text{a}$, м/с$^2$<br>Уравнение скорости<br>Уравнение перемещения<br>Характер движения тела</p><p>Рис. 110</p><p><strong>2.</strong> Дано уравнение движения тела: $x = -3 - t - t^2$ (м). Заполните таблицу и постройте график скорости движения тела.</p><p>Начальная координата $x_0$, м<br>Начальная скорость $v_0$, м/с<br>Ускорение $\text{a}$, м/с$^2$<br>Уравнение скорости<br>Уравнение перемещения<br>Характер движения тела</p>" "img" => array:1 [ 0 => array:5 [ "name" => "8-1.jpg" "alt" => null "width" => "1490" "height" => 1095 "path" => "/media/fizika_09/maron-dm/0-cp05/8-1.webp?ts=1758964220" ] ] ] #original: array:7 [ "id" => 1682932 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1090} "task" => array:2 [ "refs" => "1428617" "type" => "task" ] "text" => "<p><strong>1.</strong> Заполните таблицу, используя график скорости движения тела (рис. 110).</p><p>Начальная скорость $v_0$, м/с<br>Ускорение $\text{a}$, м/с$^2$<br>Уравнение скорости<br>Уравнение перемещения<br>Характер движения тела</p><p>Рис. 110</p><p><strong>2.</strong> Дано уравнение движения тела: $x = -3 - t - t^2$ (м). Заполните таблицу и постройте график скорости движения тела.</p><p>Начальная координата $x_0$, м<br>Начальная скорость $v_0$, м/с<br>Ускорение $\text{a}$, м/с$^2$<br>Уравнение скорости<br>Уравнение перемещения<br>Характер движения тела</p>" "img" => array:1 [ 0 => array:5 [ "name" => "8-1.jpg" "alt" => null "width" => "1490" "height" => 1095 "path" => "/media/fizika_09/maron-dm/0-cp05/8-1.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 {#1093 #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" => 1730634 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1084 #items: array:1 [ 0 => App\Models\Edition {#1092 #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 {#1088 #items: array:1 [ 0 => App\Models\Term {#1091 #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 {#1089 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1086 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1087 #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 {#1088} "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 {#1089} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1086} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1087} "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" => "1428617" "type" => "task" ] "text" => "<p><strong>1.</strong> Заполните таблицу, используя график скорости движения тела (рис. 110).</p><p><strong>Дано:</strong></p><p>График зависимости скорости от времени $v(t)$.</p><p>Из графика: $v(0) = 10$ м/с; $v(5) = 5$ м/с.</p><p><strong>Найти:</strong></p><p>Начальную скорость $v_0$, ускорение $\text{a}$, уравнение скорости $v(t)$, уравнение перемещения $s(t)$, характер движения.</p><p><strong>Решение:</strong></p><p><strong>Начальная скорость $v_0$, м/с</strong></p><p>Начальная скорость — это скорость тела в начальный момент времени $t=0$. По графику определяем, что при $t=0$ скорость $v = 10$ м/с.</p><p><strong>Ответ:</strong> 10 м/с.</p><p><strong>Ускорение a, м/с²</strong></p><p>Так как график скорости является прямой линией, движение является равнопеременным. Ускорение постоянно и равно тангенсу угла наклона графика к оси времени. Его можно вычислить по формуле: $a = \frac{\Delta v}{\Delta t} = \frac{v - v_0}{t - t_0}$.</p><p>Возьмем две точки с графика: $(t_0=0 \text{ с}, v_0=10 \text{ м/с})$ и $(t=5 \text{ с}, v=5 \text{ м/с})$.</p><p>$a = \frac{5 \text{ м/с} - 10 \text{ м/с}}{5 \text{ с} - 0 \text{ с}} = \frac{-5 \text{ м/с}}{5 \text{ с}} = -1 \text{ м/с}^2$.</p><p><strong>Ответ:</strong> -1 м/с².</p><p><strong>Уравнение скорости</strong></p><p>Общий вид уравнения скорости для равнопеременного движения: $v(t) = v_0 + at$. Подставив найденные значения $v_0 = 10$ м/с и $a = -1$ м/с², получаем:</p><p>$v(t) = 10 - 1 \cdot t$.</p><p><strong>Ответ:</strong> $v = 10 - t$ (м/с).</p><p><strong>Уравнение перемещения</strong></p><p>Общий вид уравнения перемещения для равнопеременного движения: $s(t) = v_0 t + \frac{at^2}{2}$. Подставив найденные значения $v_0$ и $\text{a}$, получаем:</p><p>$s(t) = 10t + \frac{(-1)t^2}{2} = 10t - 0.5t^2$.</p><p><strong>Ответ:</strong> $s = 10t - 0.5t^2$ (м).</p><p><strong>Характер движения тела</strong></p><p>Начальная скорость тела положительна ($v_0 = 10$ м/с), а ускорение отрицательно ($a = -1$ м/с²). Поскольку вектор ускорения направлен противоположно вектору начальной скорости, модуль скорости тела уменьшается. Такое движение называется равнозамедленным.</p><p><strong>Ответ:</strong> Равнозамедленное.</p><p><strong>2.</strong> Дано уравнение движения тела: $x = -3 - t - t^2$ (м). Заполните таблицу и постройте график скорости движения тела.</p><p><strong>Дано:</strong></p><p>Уравнение движения $x(t) = -3 - t - t^2$ (м).</p><p><strong>Найти:</strong></p><p>Начальную координату $x_0$, начальную скорость $v_0$, ускорение $\text{a}$, уравнение скорости $v(t)$, уравнение перемещения $s(t)$, характер движения, построить график $v(t)$.</p><p><strong>Решение:</strong></p><p>Сравним данное уравнение с общим видом уравнения равнопеременного движения: $x(t) = x_0 + v_0 t + \frac{at^2}{2}$.</p><p><strong>Начальная координата $x_0$, м</strong></p><p>Из сравнения уравнений видно, что свободный член, соответствующий начальной координате, равен -3.</p><p><strong>Ответ:</strong> -3 м.</p><p><strong>Начальная скорость $v_0$, м/с</strong></p><p>Коэффициент при $\text{t}$ в первой степени соответствует начальной скорости $v_0$. В данном уравнении он равен -1.</p><p><strong>Ответ:</strong> -1 м/с.</p><p><strong>Ускорение a, м/с²</strong></p><p>Коэффициент при $t^2$ равен $\frac{a}{2}$. В данном уравнении он равен -1, следовательно:</p><p>$\frac{a}{2} = -1 \implies a = -2 \text{ м/с}^2$.</p><p><strong>Ответ:</strong> -2 м/с².</p><p><strong>Уравнение скорости</strong></p><p>Подставим найденные значения $v_0 = -1$ м/с и $a = -2$ м/с² в общую формулу скорости $v(t) = v_0 + at$:</p><p>$v(t) = -1 + (-2)t = -1 - 2t$.</p><p><strong>Ответ:</strong> $v = -1 - 2t$ (м/с).</p><p><strong>Уравнение перемещения</strong></p><p>Перемещение $s(t)$ можно найти по формуле $s(t) = v_0 t + \frac{at^2}{2}$ или как разность $s(t) = x(t) - x_0$.</p><p>$s(t) = (-3 - t - t^2) - (-3) = -t - t^2$.</p><p><strong>Ответ:</strong> $s = -t - t^2$ (м).</p><p><strong>Характер движения тела</strong></p><p>Начальная скорость $v_0 = -1$ м/с и ускорение $a = -2$ м/с² имеют одинаковый знак (оба отрицательны). Это означает, что вектор ускорения направлен в ту же сторону, что и вектор начальной скорости. Следовательно, модуль скорости со временем увеличивается. Движение является равноускоренным и направлено против положительного направления оси X.</p><p><strong>Ответ:</strong> Равноускоренное.</p><p><strong>График скорости движения тела</strong></p><p>Уравнение скорости $v(t) = -1 - 2t$ представляет собой линейную функцию. Для построения графика найдем две точки:</p><ul><li>при $t=0$, $v = -1 - 2 \cdot 0 = -1$ м/с. Точка (0; -1).</li><li>при $t=2$, $v = -1 - 2 \cdot 2 = -5$ м/с. Точка (2; -5).</li></ul><p>Проводим прямую через эти две точки.</p><svg width="400" height="350" viewBox="-50 -280 350 300" xmlns="http://www.w3.org/2000/svg"><defs><marker id="arrowhead" markerWidth="10" markerHeight="7" refX="0" refY="3.5" orient="auto"><polygon points="0 0, 10 3.5, 0 7" fill="black"></polygon></marker></defs><line x1="0" y1="0" x2="300" y2="0" stroke="black" stroke-width="2" marker-end="url(#arrowhead)"></line><line x1="0" y1="20" x2="0" y2="-250" stroke="black" stroke-width="2" marker-end="url(#arrowhead)"></line><text x="310" y="5" font-family="Arial" font-size="16">t, c</text><text x="5" y="-255" font-family="Arial" font-size="16">v, м/с</text><g stroke="lightgray" stroke-width="1"><line x1="50" y1="10" x2="50" y2="-250"></line><line x1="100" y1="10" x2="100" y2="-250"></line><line x1="150" y1="10" x2="150" y2="-250"></line><line x1="200" y1="10" x2="200" y2="-250"></line><line x1="250" y1="10" x2="250" y2="-250"></line></g><g font-family="Arial" font-size="14" text-anchor="middle"><text x="0" y="20">0</text><text x="50" y="20">1</text><text x="100" y="20">2</text><text x="150" y="20">3</text><text x="200" y="20">4</text><text x="250" y="20">5</text></g><g stroke="lightgray" stroke-width="1"><line x1="-10" y1="-40" x2="300" y2="-40"></line><line x1="-10" y1="-80" x2="300" y2="-80"></line><line x1="-10" y1="-120" x2="300" y2="-120"></line><line x1="-10" y1="-160" x2="300" y2="-160"></line><line x1="-10" y1="-200" x2="300" y2="-200"></line></g><g font-family="Arial" font-size="14" text-anchor="end"><text x="-5" y="-35">-2</text><text x="-5" y="-75">-4</text><text x="-5" y="-115">-6</text><text x="-5" y="-155">-8</text><text x="-5" y="-195">-10</text></g><line x1="0" y1="-20" x2="250" y2="-220" stroke="blue" stroke-width="3"></line></svg>" ] #original: array:6 [ "id" => 1730634 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1084} "task" => array:2 [ "refs" => "1428617" "type" => "task" ] "text" => "<p><strong>1.</strong> Заполните таблицу, используя график скорости движения тела (рис. 110).</p><p><strong>Дано:</strong></p><p>График зависимости скорости от времени $v(t)$.</p><p>Из графика: $v(0) = 10$ м/с; $v(5) = 5$ м/с.</p><p><strong>Найти:</strong></p><p>Начальную скорость $v_0$, ускорение $\text{a}$, уравнение скорости $v(t)$, уравнение перемещения $s(t)$, характер движения.</p><p><strong>Решение:</strong></p><p><strong>Начальная скорость $v_0$, м/с</strong></p><p>Начальная скорость — это скорость тела в начальный момент времени $t=0$. По графику определяем, что при $t=0$ скорость $v = 10$ м/с.</p><p><strong>Ответ:</strong> 10 м/с.</p><p><strong>Ускорение a, м/с²</strong></p><p>Так как график скорости является прямой линией, движение является равнопеременным. Ускорение постоянно и равно тангенсу угла наклона графика к оси времени. Его можно вычислить по формуле: $a = \frac{\Delta v}{\Delta t} = \frac{v - v_0}{t - t_0}$.</p><p>Возьмем две точки с графика: $(t_0=0 \text{ с}, v_0=10 \text{ м/с})$ и $(t=5 \text{ с}, v=5 \text{ м/с})$.</p><p>$a = \frac{5 \text{ м/с} - 10 \text{ м/с}}{5 \text{ с} - 0 \text{ с}} = \frac{-5 \text{ м/с}}{5 \text{ с}} = -1 \text{ м/с}^2$.</p><p><strong>Ответ:</strong> -1 м/с².</p><p><strong>Уравнение скорости</strong></p><p>Общий вид уравнения скорости для равнопеременного движения: $v(t) = v_0 + at$. Подставив найденные значения $v_0 = 10$ м/с и $a = -1$ м/с², получаем:</p><p>$v(t) = 10 - 1 \cdot t$.</p><p><strong>Ответ:</strong> $v = 10 - t$ (м/с).</p><p><strong>Уравнение перемещения</strong></p><p>Общий вид уравнения перемещения для равнопеременного движения: $s(t) = v_0 t + \frac{at^2}{2}$. Подставив найденные значения $v_0$ и $\text{a}$, получаем:</p><p>$s(t) = 10t + \frac{(-1)t^2}{2} = 10t - 0.5t^2$.</p><p><strong>Ответ:</strong> $s = 10t - 0.5t^2$ (м).</p><p><strong>Характер движения тела</strong></p><p>Начальная скорость тела положительна ($v_0 = 10$ м/с), а ускорение отрицательно ($a = -1$ м/с²). Поскольку вектор ускорения направлен противоположно вектору начальной скорости, модуль скорости тела уменьшается. Такое движение называется равнозамедленным.</p><p><strong>Ответ:</strong> Равнозамедленное.</p><p><strong>2.</strong> Дано уравнение движения тела: $x = -3 - t - t^2$ (м). Заполните таблицу и постройте график скорости движения тела.</p><p><strong>Дано:</strong></p><p>Уравнение движения $x(t) = -3 - t - t^2$ (м).</p><p><strong>Найти:</strong></p><p>Начальную координату $x_0$, начальную скорость $v_0$, ускорение $\text{a}$, уравнение скорости $v(t)$, уравнение перемещения $s(t)$, характер движения, построить график $v(t)$.</p><p><strong>Решение:</strong></p><p>Сравним данное уравнение с общим видом уравнения равнопеременного движения: $x(t) = x_0 + v_0 t + \frac{at^2}{2}$.</p><p><strong>Начальная координата $x_0$, м</strong></p><p>Из сравнения уравнений видно, что свободный член, соответствующий начальной координате, равен -3.</p><p><strong>Ответ:</strong> -3 м.</p><p><strong>Начальная скорость $v_0$, м/с</strong></p><p>Коэффициент при $\text{t}$ в первой степени соответствует начальной скорости $v_0$. В данном уравнении он равен -1.</p><p><strong>Ответ:</strong> -1 м/с.</p><p><strong>Ускорение a, м/с²</strong></p><p>Коэффициент при $t^2$ равен $\frac{a}{2}$. В данном уравнении он равен -1, следовательно:</p><p>$\frac{a}{2} = -1 \implies a = -2 \text{ м/с}^2$.</p><p><strong>Ответ:</strong> -2 м/с².</p><p><strong>Уравнение скорости</strong></p><p>Подставим найденные значения $v_0 = -1$ м/с и $a = -2$ м/с² в общую формулу скорости $v(t) = v_0 + at$:</p><p>$v(t) = -1 + (-2)t = -1 - 2t$.</p><p><strong>Ответ:</strong> $v = -1 - 2t$ (м/с).</p><p><strong>Уравнение перемещения</strong></p><p>Перемещение $s(t)$ можно найти по формуле $s(t) = v_0 t + \frac{at^2}{2}$ или как разность $s(t) = x(t) - x_0$.</p><p>$s(t) = (-3 - t - t^2) - (-3) = -t - t^2$.</p><p><strong>Ответ:</strong> $s = -t - t^2$ (м).</p><p><strong>Характер движения тела</strong></p><p>Начальная скорость $v_0 = -1$ м/с и ускорение $a = -2$ м/с² имеют одинаковый знак (оба отрицательны). Это означает, что вектор ускорения направлен в ту же сторону, что и вектор начальной скорости. Следовательно, модуль скорости со временем увеличивается. Движение является равноускоренным и направлено против положительного направления оси X.</p><p><strong>Ответ:</strong> Равноускоренное.</p><p><strong>График скорости движения тела</strong></p><p>Уравнение скорости $v(t) = -1 - 2t$ представляет собой линейную функцию. Для построения графика найдем две точки:</p><ul><li>при $t=0$, $v = -1 - 2 \cdot 0 = -1$ м/с. Точка (0; -1).</li><li>при $t=2$, $v = -1 - 2 \cdot 2 = -5$ м/с. Точка (2; -5).</li></ul><p>Проводим прямую через эти две точки.</p><svg width="400" height="350" viewBox="-50 -280 350 300" xmlns="http://www.w3.org/2000/svg"><defs><marker id="arrowhead" markerWidth="10" markerHeight="7" refX="0" refY="3.5" orient="auto"><polygon points="0 0, 10 3.5, 0 7" fill="black"></polygon></marker></defs><line x1="0" y1="0" x2="300" y2="0" stroke="black" stroke-width="2" marker-end="url(#arrowhead)"></line><line x1="0" y1="20" x2="0" y2="-250" stroke="black" stroke-width="2" marker-end="url(#arrowhead)"></line><text x="310" y="5" font-family="Arial" font-size="16">t, c</text><text x="5" y="-255" font-family="Arial" font-size="16">v, м/с</text><g stroke="lightgray" stroke-width="1"><line x1="50" y1="10" x2="50" y2="-250"></line><line x1="100" y1="10" x2="100" y2="-250"></line><line x1="150" y1="10" x2="150" y2="-250"></line><line x1="200" y1="10" x2="200" y2="-250"></line><line x1="250" y1="10" x2="250" y2="-250"></line></g><g font-family="Arial" font-size="14" text-anchor="middle"><text x="0" y="20">0</text><text x="50" y="20">1</text><text x="100" y="20">2</text><text x="150" y="20">3</text><text x="200" y="20">4</text><text x="250" y="20">5</text></g><g stroke="lightgray" stroke-width="1"><line x1="-10" y1="-40" x2="300" y2="-40"></line><line x1="-10" y1="-80" x2="300" y2="-80"></line><line x1="-10" y1="-120" x2="300" y2="-120"></line><line x1="-10" y1="-160" x2="300" y2="-160"></line><line x1="-10" y1="-200" x2="300" y2="-200"></line></g><g font-family="Arial" font-size="14" text-anchor="end"><text x="-5" y="-35">-2</text><text x="-5" y="-75">-4</text><text x="-5" y="-115">-6</text><text x="-5" y="-155">-8</text><text x="-5" y="-195">-10</text></g><line x1="0" y1="-20" x2="250" y2="-220" stroke="blue" stroke-width="3"></line></svg>" ] #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" => "1428618" "type" => "task" ] "previous" => array:2 [ "refs" => "1428616" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1103 #items: array:1 [ 0 => App\Models\Book {#1119} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1077 #items: array:1 [ 0 => App\Models\BookPage {#1076 #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" => 1428959 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "68" "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/page-68" "field_display_title" => "68" "field_folder" => "1" "field_image_name" => "68" 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Вариант 8 (с. 68)
Условие. Вариант 8 (с. 68)
скриншот условия
1. Заполните таблицу, используя график скорости движения тела (рис. 110).
Начальная скорость $v_0$, м/с
Ускорение $\text{a}$, м/с$^2$
Уравнение скорости
Уравнение перемещения
Характер движения тела
Рис. 110
2. Дано уравнение движения тела: $x = -3 - t - t^2$ (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 8 (с. 68)
1. Заполните таблицу, используя график скорости движения тела (рис. 110).
Дано:
График зависимости скорости от времени $v(t)$.
Из графика: $v(0) = 10$ м/с; $v(5) = 5$ м/с.
Найти:
Начальную скорость $v_0$, ускорение $\text{a}$, уравнение скорости $v(t)$, уравнение перемещения $s(t)$, характер движения.
Решение:
Начальная скорость $v_0$, м/с
Начальная скорость — это скорость тела в начальный момент времени $t=0$. По графику определяем, что при $t=0$ скорость $v = 10$ м/с.
Ответ: 10 м/с.
Ускорение a, м/с²
Так как график скорости является прямой линией, движение является равнопеременным. Ускорение постоянно и равно тангенсу угла наклона графика к оси времени. Его можно вычислить по формуле: $a = \frac{\Delta v}{\Delta t} = \frac{v - v_0}{t - t_0}$.
Возьмем две точки с графика: $(t_0=0 \text{ с}, v_0=10 \text{ м/с})$ и $(t=5 \text{ с}, v=5 \text{ м/с})$.
$a = \frac{5 \text{ м/с} - 10 \text{ м/с}}{5 \text{ с} - 0 \text{ с}} = \frac{-5 \text{ м/с}}{5 \text{ с}} = -1 \text{ м/с}^2$.
Ответ: -1 м/с².
Уравнение скорости
Общий вид уравнения скорости для равнопеременного движения: $v(t) = v_0 + at$. Подставив найденные значения $v_0 = 10$ м/с и $a = -1$ м/с², получаем:
$v(t) = 10 - 1 \cdot t$.
Ответ: $v = 10 - t$ (м/с).
Уравнение перемещения
Общий вид уравнения перемещения для равнопеременного движения: $s(t) = v_0 t + \frac{at^2}{2}$. Подставив найденные значения $v_0$ и $\text{a}$, получаем:
$s(t) = 10t + \frac{(-1)t^2}{2} = 10t - 0.5t^2$.
Ответ: $s = 10t - 0.5t^2$ (м).
Характер движения тела
Начальная скорость тела положительна ($v_0 = 10$ м/с), а ускорение отрицательно ($a = -1$ м/с²). Поскольку вектор ускорения направлен противоположно вектору начальной скорости, модуль скорости тела уменьшается. Такое движение называется равнозамедленным.
Ответ: Равнозамедленное.
2. Дано уравнение движения тела: $x = -3 - t - t^2$ (м). Заполните таблицу и постройте график скорости движения тела.
Дано:
Уравнение движения $x(t) = -3 - t - t^2$ (м).
Найти:
Начальную координату $x_0$, начальную скорость $v_0$, ускорение $\text{a}$, уравнение скорости $v(t)$, уравнение перемещения $s(t)$, характер движения, построить график $v(t)$.
Решение:
Сравним данное уравнение с общим видом уравнения равнопеременного движения: $x(t) = x_0 + v_0 t + \frac{at^2}{2}$.
Начальная координата $x_0$, м
Из сравнения уравнений видно, что свободный член, соответствующий начальной координате, равен -3.
Ответ: -3 м.
Начальная скорость $v_0$, м/с
Коэффициент при $\text{t}$ в первой степени соответствует начальной скорости $v_0$. В данном уравнении он равен -1.
Ответ: -1 м/с.
Ускорение a, м/с²
Коэффициент при $t^2$ равен $\frac{a}{2}$. В данном уравнении он равен -1, следовательно:
$\frac{a}{2} = -1 \implies a = -2 \text{ м/с}^2$.
Ответ: -2 м/с².
Уравнение скорости
Подставим найденные значения $v_0 = -1$ м/с и $a = -2$ м/с² в общую формулу скорости $v(t) = v_0 + at$:
$v(t) = -1 + (-2)t = -1 - 2t$.
Ответ: $v = -1 - 2t$ (м/с).
Уравнение перемещения
Перемещение $s(t)$ можно найти по формуле $s(t) = v_0 t + \frac{at^2}{2}$ или как разность $s(t) = x(t) - x_0$.
$s(t) = (-3 - t - t^2) - (-3) = -t - t^2$.
Ответ: $s = -t - t^2$ (м).
Характер движения тела
Начальная скорость $v_0 = -1$ м/с и ускорение $a = -2$ м/с² имеют одинаковый знак (оба отрицательны). Это означает, что вектор ускорения направлен в ту же сторону, что и вектор начальной скорости. Следовательно, модуль скорости со временем увеличивается. Движение является равноускоренным и направлено против положительного направления оси X.
Ответ: Равноускоренное.
График скорости движения тела
Уравнение скорости $v(t) = -1 - 2t$ представляет собой линейную функцию. Для построения графика найдем две точки:
- при $t=0$, $v = -1 - 2 \cdot 0 = -1$ м/с. Точка (0; -1).
- при $t=2$, $v = -1 - 2 \cdot 2 = -5$ м/с. Точка (2; -5).
Проводим прямую через эти две точки.
Другие задания:
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