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Номер 8.15, страница 41 - гдз по физике 8 класс задачник Артеменков, Ломаченков
Авторы: Артеменков Д. А., Ломаченков И. А., Панебратцев Ю. А.
Тип: Задачник
Серия: сферы
Издательство: Просвещение
Год издания: 2010 - 2026
Цвет обложки: фиолетовый
ISBN: 978-5-09-046040-8
Популярные ГДЗ в 8 классе
VIII. Основы кинематики - номер 8.15, страница 41.
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" => 1460311 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "41" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/08-15" "field_display_title" => "8.15" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #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" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #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 "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1073 #items: array:1 [ 0 => App\Models\Branch {#1034 #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" => 1460051 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "VIII. Основы кинематики" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "39" "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 {#1038 #items: array:1 [ 0 => App\Models\Book {#1040 #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" => 1646 "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 {#1041 #items: array:1 [ 0 => App\Models\Term {#1042 #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 {#1043 #items: array:1 [ 0 => App\Models\Term {#1044 #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 {#1045 #items: array:1 [ 0 => App\Models\Term {#1046 #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 {#1047 #items: array:3 [ 0 => 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] } 1 => App\Models\Term {#1049 #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] } 2 => App\Models\Term {#1050 #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 {#1051 #items: [] #escapeWhenCastingToString: false } "field_book_type" => 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 [ …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 {#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_city" => Illuminate\Database\Eloquent\Collection {#1056 #items: array:1 [ 0 => App\Models\Term {#1057 #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 {#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:8 [ …8] #original: array:8 [ …8] #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_umk" => Illuminate\Database\Eloquent\Collection {#1060 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1061 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1062 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => "5" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1063 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064 #items: array:1 [ 0 => App\Models\Term {#1050} ] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2010" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "308" "field_priority" => null "field_default_folder" => "/fizika_08/artemenkov-zd/" "field_isbn" => "978-5-09-046040-8" "field_cover" => array:1 [ 0 => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" "alt" => "" "width" => "1891" "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" => "/8-klass/fizika/artemenkov-zadachnik" "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" => 379 "subject" => 556 "class_subject" => 492 ] ] #original: array:50 [ "id" => 1646 "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 {#1041} "field_class" => Illuminate\Database\Eloquent\Collection {#1043} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045} "field_author" => Illuminate\Database\Eloquent\Collection {#1047} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1051} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1052} "field_country" => Illuminate\Database\Eloquent\Collection {#1054} "field_city" => Illuminate\Database\Eloquent\Collection {#1056} "field_series" => Illuminate\Database\Eloquent\Collection {#1058} "field_umk" => Illuminate\Database\Eloquent\Collection {#1060} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1061} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1062} "field_publication_number" => "5" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1063} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2010" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "308" "field_priority" => null "field_default_folder" => "/fizika_08/artemenkov-zd/" "field_isbn" => "978-5-09-046040-8" "field_cover" => array:1 [ 0 => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" "alt" => "" "width" => "1891" "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" => "/8-klass/fizika/artemenkov-zadachnik" "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" => 379 "subject" => 556 "class_subject" => 492 ] ] #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" => 1460051 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "VIII. Основы кинематики" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039} "field_page_start" => "39" "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 {#1038} "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 {#1071 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1074 #items: array:2 [ 0 => App\Models\Element {#1083 #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" => 1753809 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1092 #items: array:1 [ 0 => App\Models\Edition {#1084 #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" => 6390 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1086 #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, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "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 {#1087 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1088 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1089 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6390 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1086} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "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 {#1087} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1088} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1089} "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" => "1460311" "type" => "task" ] "text" => "<p><strong>8.15</strong> На рисунке 33 приведены графики зависимости скорости прямолинейного равномерного движения от времени $v(t)$. Постройте соответствующие им графики зависимости перемещения от времени $s(t)$, считая, что перемещение $s=0$ в момент времени $t=0$.</p><p>Рис. 33</p>" "img" => array:2 [ 0 => array:5 [ "name" => "15-1.jpg" "alt" => null "width" => "1759" "height" => 365 "path" => "/media/fizika_08/artemenkov-zd/0-08/15-1.webp?ts=1760701788" ] 1 => array:5 [ "name" => "15-2.jpg" "alt" => null "width" => "773" "height" => 829 "path" => "/media/fizika_08/artemenkov-zd/0-08/15-2.webp?ts=1760701788" ] ] ] #original: array:7 [ "id" => 1753809 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1092} "task" => array:2 [ "refs" => "1460311" "type" => "task" ] "text" => "<p><strong>8.15</strong> На рисунке 33 приведены графики зависимости скорости прямолинейного равномерного движения от времени $v(t)$. Постройте соответствующие им графики зависимости перемещения от времени $s(t)$, считая, что перемещение $s=0$ в момент времени $t=0$.</p><p>Рис. 33</p>" "img" => array:2 [ 0 => array:5 [ "name" => "15-1.jpg" "alt" => null "width" => "1759" "height" => 365 "path" => "/media/fizika_08/artemenkov-zd/0-08/15-1.webp?ts=1760701788" ] 1 => array:5 [ "name" => "15-2.jpg" "alt" => null "width" => "773" "height" => 829 "path" => "/media/fizika_08/artemenkov-zd/0-08/15-2.webp?ts=1760701788" ] ] ] #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 {#1090 #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" => 1821916 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1100 #items: array:1 [ 0 => App\Models\Edition {#1091 #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" => 6688 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1094 #items: array:1 [ 0 => App\Models\Term {#1093 #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" => "0" "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 {#1095 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1096 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1097 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6688 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1094} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "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 {#1095} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1096} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1097} "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" => "1460311" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>На рисунке приведены графики зависимости скорости от времени $v(t)$ для трех случаев прямолинейного равномерного движения:</p><p><strong>1.</strong> Скорость $v_1 = 30$ м/с в интервале времени от $t=0$ с до $t_1=20$ с.</p><p><strong>2.</strong> Скорость $v_2 = 20$ м/с в интервале времени от $t=0$ с до $t_2=30$ с.</p><p><strong>3.</strong> Скорость $v_3 = 10$ м/с в интервале времени от $t=0$ с до $t_3=60$ с.</p><p>Начальное перемещение в момент времени $t=0$ равно нулю: $s(0) = 0$.</p><p><strong>Найти:</strong></p><p>Построить графики зависимости перемещения от времени $s(t)$ для каждого случая.</p><p><strong>Решение:</strong></p><p>При прямолинейном равномерном движении перемещение тела можно рассчитать по формуле $s = v \cdot t + s_0$, где $\text{v}$ – постоянная скорость, $\text{t}$ – время, а $s_0$ – начальное перемещение. Согласно условию задачи, $s_0 = 0$ в момент времени $t=0$. Таким образом, зависимость перемещения от времени для каждого случая будет описываться уравнением $s(t) = v \cdot t$. Это уравнение представляет собой линейную функцию, график которой – прямая линия, проходящая через начало координат. Угол наклона этой прямой к оси времени определяется скоростью движения: чем выше скорость, тем больше угол наклона.</p><p><strong>1</strong> Для первого тела скорость $v_1 = 30$ м/с. Уравнение движения имеет вид: $s_1(t) = 30t$.</p><p>Найдем конечное перемещение в момент времени $t_1 = 20$ с:</p><p>$s_1(20) = 30 \text{ м/с} \cdot 20 \text{ с} = 600$ м.</p><p>Для построения графика $s_1(t)$ необходимо соединить отрезком прямой две точки: начальную $(0 \text{ с}; 0 \text{ м})$ и конечную $(20 \text{ с}; 600 \text{ м})$.</p><p><strong>Ответ:</strong> График зависимости перемещения от времени для первого случая представляет собой отрезок прямой, проведенный из начала координат $(0 \text{ с}, 0 \text{ м})$ в точку $(20 \text{ с}, 600 \text{ м})$.</p><p><strong>2</strong> Для второго тела скорость $v_2 = 20$ м/с. Уравнение движения имеет вид: $s_2(t) = 20t$.</p><p>Найдем конечное перемещение в момент времени $t_2 = 30$ с:</p><p>$s_2(30) = 20 \text{ м/с} \cdot 30 \text{ с} = 600$ м.</p><p>Для построения графика $s_2(t)$ необходимо соединить отрезком прямой две точки: начальную $(0 \text{ с}; 0 \text{ м})$ и конечную $(30 \text{ с}; 600 \text{ м})$.</p><p><strong>Ответ:</strong> График зависимости перемещения от времени для второго случая представляет собой отрезок прямой, проведенный из начала координат $(0 \text{ с}, 0 \text{ м})$ в точку $(30 \text{ с}, 600 \text{ м})$.</p><p><strong>3</strong> Для третьего тела скорость $v_3 = 10$ м/с. Уравнение движения имеет вид: $s_3(t) = 10t$.</p><p>Найдем конечное перемещение в момент времени $t_3 = 60$ с:</p><p>$s_3(60) = 10 \text{ м/с} \cdot 60 \text{ с} = 600$ м.</p><p>Для построения графика $s_3(t)$ необходимо соединить отрезком прямой две точки: начальную $(0 \text{ с}; 0 \text{ м})$ и конечную $(60 \text{ с}; 600 \text{ м})$.</p><p><strong>Ответ:</strong> График зависимости перемещения от времени для третьего случая представляет собой отрезок прямой, проведенный из начала координат $(0 \text{ с}, 0 \text{ м})$ в точку $(60 \text{ с}, 600 \text{ м})$.</p>" ] #original: array:6 [ "id" => 1821916 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1100} "task" => array:2 [ "refs" => "1460311" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>На рисунке приведены графики зависимости скорости от времени $v(t)$ для трех случаев прямолинейного равномерного движения:</p><p><strong>1.</strong> Скорость $v_1 = 30$ м/с в интервале времени от $t=0$ с до $t_1=20$ с.</p><p><strong>2.</strong> Скорость $v_2 = 20$ м/с в интервале времени от $t=0$ с до $t_2=30$ с.</p><p><strong>3.</strong> Скорость $v_3 = 10$ м/с в интервале времени от $t=0$ с до $t_3=60$ с.</p><p>Начальное перемещение в момент времени $t=0$ равно нулю: $s(0) = 0$.</p><p><strong>Найти:</strong></p><p>Построить графики зависимости перемещения от времени $s(t)$ для каждого случая.</p><p><strong>Решение:</strong></p><p>При прямолинейном равномерном движении перемещение тела можно рассчитать по формуле $s = v \cdot t + s_0$, где $\text{v}$ – постоянная скорость, $\text{t}$ – время, а $s_0$ – начальное перемещение. Согласно условию задачи, $s_0 = 0$ в момент времени $t=0$. Таким образом, зависимость перемещения от времени для каждого случая будет описываться уравнением $s(t) = v \cdot t$. Это уравнение представляет собой линейную функцию, график которой – прямая линия, проходящая через начало координат. Угол наклона этой прямой к оси времени определяется скоростью движения: чем выше скорость, тем больше угол наклона.</p><p><strong>1</strong> Для первого тела скорость $v_1 = 30$ м/с. Уравнение движения имеет вид: $s_1(t) = 30t$.</p><p>Найдем конечное перемещение в момент времени $t_1 = 20$ с:</p><p>$s_1(20) = 30 \text{ м/с} \cdot 20 \text{ с} = 600$ м.</p><p>Для построения графика $s_1(t)$ необходимо соединить отрезком прямой две точки: начальную $(0 \text{ с}; 0 \text{ м})$ и конечную $(20 \text{ с}; 600 \text{ м})$.</p><p><strong>Ответ:</strong> График зависимости перемещения от времени для первого случая представляет собой отрезок прямой, проведенный из начала координат $(0 \text{ с}, 0 \text{ м})$ в точку $(20 \text{ с}, 600 \text{ м})$.</p><p><strong>2</strong> Для второго тела скорость $v_2 = 20$ м/с. Уравнение движения имеет вид: $s_2(t) = 20t$.</p><p>Найдем конечное перемещение в момент времени $t_2 = 30$ с:</p><p>$s_2(30) = 20 \text{ м/с} \cdot 30 \text{ с} = 600$ м.</p><p>Для построения графика $s_2(t)$ необходимо соединить отрезком прямой две точки: начальную $(0 \text{ с}; 0 \text{ м})$ и конечную $(30 \text{ с}; 600 \text{ м})$.</p><p><strong>Ответ:</strong> График зависимости перемещения от времени для второго случая представляет собой отрезок прямой, проведенный из начала координат $(0 \text{ с}, 0 \text{ м})$ в точку $(30 \text{ с}, 600 \text{ м})$.</p><p><strong>3</strong> Для третьего тела скорость $v_3 = 10$ м/с. Уравнение движения имеет вид: $s_3(t) = 10t$.</p><p>Найдем конечное перемещение в момент времени $t_3 = 60$ с:</p><p>$s_3(60) = 10 \text{ м/с} \cdot 60 \text{ с} = 600$ м.</p><p>Для построения графика $s_3(t)$ необходимо соединить отрезком прямой две точки: начальную $(0 \text{ с}; 0 \text{ м})$ и конечную $(60 \text{ с}; 600 \text{ м})$.</p><p><strong>Ответ:</strong> График зависимости перемещения от времени для третьего случая представляет собой отрезок прямой, проведенный из начала координат $(0 \text{ с}, 0 \text{ м})$ в точку $(60 \text{ с}, 600 \text{ м})$.</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" => "1460312" "type" => "task" ] "previous" => array:2 [ "refs" => "1460310" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1123 #items: array:1 [ 0 => App\Models\Book {#1080 #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" => 1646 "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 {#1072 #items: array:1 [ 0 => App\Models\Term {#1075 #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 {#1082 #items: array:1 [ 0 => App\Models\Term {#1078 #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" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ "field_accusative_case" => "восьмой" "field_creative_case" => "восьмым" "field_dative_case" => "восьмому" "field_genitive_case" => "восьмого" "field_nominative_case" => "восьмой" "field_prepositional_case" => "восьмом" ] "field_translit" => "vosmoj" ] #original: array:6 [ "id" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ "field_accusative_case" => "восьмой" "field_creative_case" => "восьмым" "field_dative_case" => "восьмому" "field_genitive_case" => "восьмого" "field_nominative_case" => "восьмой" "field_prepositional_case" => "восьмом" ] "field_translit" => "vosmoj" ] #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 {#1076 #items: array:1 [ 0 => App\Models\Term {#1079 #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 {#1077 #items: array:3 [ 0 => App\Models\Term {#1098 #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" => 3745 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Артеменков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Денис" "field_patronymic" => "Александрович" "field_surname_rp" => null ] #original: array:12 [ "id" => 3745 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Артеменков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Денис" "field_patronymic" => "Александрович" "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 {#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:12 [ "id" => 5014 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Ломаченков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Иван" "field_patronymic" => "Алексеевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 5014 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Ломаченков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Иван" "field_patronymic" => "Алексеевич" "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 => "*" ] } 2 => App\Models\Term {#1101 #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" => 5412 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Панебратцев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Юрий" "field_patronymic" => "Анатольевич" "field_surname_rp" => "Панебратцева" ] #original: array:12 [ "id" => 5412 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Панебратцев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Юрий" "field_patronymic" => "Анатольевич" "field_surname_rp" => "Панебратцева" ] #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 {#1102 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1103 #items: array:1 [ 0 => App\Models\Term {#1104 #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" => 6518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Задачник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "задачник" "field_creative_case" => "задачником" "field_dative_case" => "задачнику" "field_genitive_case" => "задачника" "field_nominative_case" => "задачник" "field_prepositional_case" => "задачнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "zadachnik" ] #original: array:10 [ "id" => 6518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Задачник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "задачник" "field_creative_case" => "задачником" "field_dative_case" => "задачнику" "field_genitive_case" => "задачника" "field_nominative_case" => "задачник" "field_prepositional_case" => "задачнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "zadachnik" ] #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 {#1105 #items: array:1 [ 0 => App\Models\Term {#1106 #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 {#1107 #items: array:1 [ 0 => App\Models\Term {#1108 #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 {#1109 #items: array:1 [ 0 => App\Models\Term {#1110 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:8 [ "id" => 4795 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "сферы" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "sfery" ] #original: array:8 [ "id" => 4795 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "сферы" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "sfery" ] #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_umk" => Illuminate\Database\Eloquent\Collection {#1111 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1112 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1113 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => "5" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1114 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1115 #items: array:1 [ 0 => App\Models\Term {#1101} ] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2010" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "308" "field_priority" => null "field_default_folder" => "/fizika_08/artemenkov-zd/" "field_isbn" => "978-5-09-046040-8" "field_cover" => array:1 [ 0 => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" "alt" => "" "width" => "1891" "height" => "2427" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1116 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1117 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1118 #items: [] #escapeWhenCastingToString: false } "field_url" => "/8-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1119 #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:6 [ "id" => 48 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "фиолетовый" "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" => "fioletovyy" ] #original: array:6 [ "id" => 48 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "фиолетовый" "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" => "fioletovyy" ] #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" => 379 "subject" => 556 "class_subject" => 492 ] ] #original: array:50 [ "id" => 1646 "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 {#1072} "field_class" => Illuminate\Database\Eloquent\Collection {#1082} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1076} "field_author" => Illuminate\Database\Eloquent\Collection {#1077} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1102} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1103} "field_country" => Illuminate\Database\Eloquent\Collection {#1105} "field_city" => Illuminate\Database\Eloquent\Collection {#1107} "field_series" => Illuminate\Database\Eloquent\Collection {#1109} "field_umk" => Illuminate\Database\Eloquent\Collection {#1111} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1112} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1113} "field_publication_number" => "5" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1114} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1115} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2010" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "308" "field_priority" => null "field_default_folder" => "/fizika_08/artemenkov-zd/" "field_isbn" => "978-5-09-046040-8" "field_cover" => array:1 [ 0 => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/artemenkov-zd/covers/cover1.webp?ts=1760136860" "alt" => "" "width" => "1891" "height" => "2427" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1116} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1117} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1118} "field_url" => "/8-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1119} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 379 "subject" => 556 "class_subject" => 492 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1128 #items: array:1 [ 0 => App\Models\BookPage {#1127 #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" => 1462338 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "41" "field_url" => "/8-klass/fizika/artemenkov-zadachnik/page-41" "field_display_title" => "41" "field_folder" => "1" "field_image_name" => "41" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1129 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1130 #items: array:1 [ 0 => App\Models\Book {#1080} ] #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 {#1131 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1141 #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" => 1753899 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1142 #items: array:1 [ 0 => App\Models\Edition {#1084} ] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1462338" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "41-1.jpg" "alt" => null "width" => "1994" "height" => 2505 "path" => "/media/fizika_08/artemenkov-zd/0-1/41-1.webp?ts=1760705538" ] ] ] #original: array:6 [ "id" => 1753899 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1142} "book_page" => array:2 [ "refs" => "1462338" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "41-1.jpg" "alt" => null "width" => "1994" "height" => 2505 "path" => "/media/fizika_08/artemenkov-zd/0-1/41-1.webp?ts=1760705538" ] ] ] #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" => "1462339" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1462337" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1226 #items: array:4 [ 0 => App\Models\Task {#1236 #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" => 1460309 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "41" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/08-13" "field_display_title" => "8.13" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1237 #items: array:1 [ 0 => App\Models\Term {#1036} ] #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 {#1238 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1239 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1240 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1242 #items: array:2 [ 0 => App\Models\Element {#1251 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true …25 } 1 => App\Models\Element {#1253 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1460310" "type" => "task" ] "previous" => array:2 [ "refs" => "1460308" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1248 #items: array:1 [ 0 => App\Models\Book {#1080} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1462338" "type" => "book_page" ] ] #original: array:24 [ "id" => 1460309 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "41" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/08-13" "field_display_title" => "8.13" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1237} "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 {#1238} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1239} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1240} "content" => Illuminate\Database\Eloquent\Collection {#1242} "next" => array:2 [ "refs" => "1460310" "type" => "task" ] "previous" => array:2 [ "refs" => "1460308" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1248} "page" => array:2 [ "refs" => "1462338" "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 {#1243 #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" => 1460310 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "41" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/08-14" "field_display_title" => "8.14" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1241 #items: array:1 [ 0 => App\Models\Term {#1036} ] #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 {#1250 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1246 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1244 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1245 #items: array:2 [ 0 => App\Models\Element {#1263 …30} 1 => App\Models\Element {#1265 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1460311" "type" => "task" ] "previous" => array:2 [ "refs" => "1460309" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1260 #items: array:1 [ 0 => App\Models\Book {#1080} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1462338" "type" => "book_page" ] ] #original: array:24 [ "id" => 1460310 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "41" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/08-14" "field_display_title" => "8.14" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1241} "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 {#1250} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1246} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1244} "content" => Illuminate\Database\Eloquent\Collection {#1245} "next" => array:2 [ "refs" => "1460311" "type" => "task" ] "previous" => array:2 [ "refs" => "1460309" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1260} "page" => array:2 [ "refs" => "1462338" "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 {#1255 #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" => 1460311 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "41" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/08-15" "field_display_title" => "8.15" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1247 #items: array:1 [ 0 => App\Models\Term {#1036} ] #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 {#1262 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1258 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1256 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1259 #items: array:2 [ 0 => App\Models\Element {#1083} 1 => App\Models\Element {#1090} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1460312" "type" => "task" ] "previous" => array:2 [ "refs" => "1460310" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1257 #items: array:1 [ 0 => App\Models\Book {#1080} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1462338" "type" => "book_page" ] ] #original: array:24 [ "id" => 1460311 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "41" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/08-15" "field_display_title" => "8.15" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1247} "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 {#1262} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1258} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1256} "content" => Illuminate\Database\Eloquent\Collection {#1259} "next" => array:2 [ "refs" => "1460312" "type" => "task" ] "previous" => array:2 [ "refs" => "1460310" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1257} "page" => array:2 [ "refs" => "1462338" "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 => "*" ] } 3 => App\Models\Task {#1267 #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" => 1460312 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "41" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/08-16" "field_display_title" => "8.16" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1268 #items: array:1 [ 0 => App\Models\Term {#1036} ] #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 {#1269 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1270 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1271 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1273 #items: array:2 [ 0 => App\Models\Element {#1282 …30} 1 => App\Models\Element {#1284 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1460313" "type" => "task" ] "previous" => array:2 [ "refs" => "1460311" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1279 #items: array:1 [ 0 => App\Models\Book {#1080} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1462338" "type" => "book_page" ] ] #original: array:24 [ "id" => 1460312 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "41" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/08-16" "field_display_title" => "8.16" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1268} "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 {#1269} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1270} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1271} "content" => Illuminate\Database\Eloquent\Collection {#1273} "next" => array:2 [ "refs" => "1460313" "type" => "task" ] "previous" => array:2 [ "refs" => "1460311" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1279} "page" => array:2 [ "refs" => "1462338" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1462338 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "41" "field_url" => "/8-klass/fizika/artemenkov-zadachnik/page-41" "field_display_title" => "41" "field_folder" => "1" "field_image_name" => "41" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1129} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1130} "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 {#1131} "content" => Illuminate\Database\Eloquent\Collection {#1141} "next" => array:2 [ "refs" => "1462339" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1462337" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1226} ] #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" => 1460311 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "41" "field_page_end" => null "field_url" => "/8-klass/fizika/artemenkov-zadachnik/08-15" "field_display_title" => "8.15" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037} "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 {#1035} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1073} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1071} "content" => Illuminate\Database\Eloquent\Collection {#1074} "next" => array:2 [ "refs" => "1460312" "type" => "task" ] "previous" => array:2 [ "refs" => "1460310" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1123} "page" => array:2 [ "refs" => "1462338" "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 => "*" ] }
№8.15 (с. 41)
Условие. №8.15 (с. 41)
скриншот условия
8.15 На рисунке 33 приведены графики зависимости скорости прямолинейного равномерного движения от времени $v(t)$. Постройте соответствующие им графики зависимости перемещения от времени $s(t)$, считая, что перемещение $s=0$ в момент времени $t=0$.
Рис. 33
Решение. №8.15 (с. 41)
Дано:
На рисунке приведены графики зависимости скорости от времени $v(t)$ для трех случаев прямолинейного равномерного движения:
1. Скорость $v_1 = 30$ м/с в интервале времени от $t=0$ с до $t_1=20$ с.
2. Скорость $v_2 = 20$ м/с в интервале времени от $t=0$ с до $t_2=30$ с.
3. Скорость $v_3 = 10$ м/с в интервале времени от $t=0$ с до $t_3=60$ с.
Начальное перемещение в момент времени $t=0$ равно нулю: $s(0) = 0$.
Найти:
Построить графики зависимости перемещения от времени $s(t)$ для каждого случая.
Решение:
При прямолинейном равномерном движении перемещение тела можно рассчитать по формуле $s = v \cdot t + s_0$, где $\text{v}$ – постоянная скорость, $\text{t}$ – время, а $s_0$ – начальное перемещение. Согласно условию задачи, $s_0 = 0$ в момент времени $t=0$. Таким образом, зависимость перемещения от времени для каждого случая будет описываться уравнением $s(t) = v \cdot t$. Это уравнение представляет собой линейную функцию, график которой – прямая линия, проходящая через начало координат. Угол наклона этой прямой к оси времени определяется скоростью движения: чем выше скорость, тем больше угол наклона.
1 Для первого тела скорость $v_1 = 30$ м/с. Уравнение движения имеет вид: $s_1(t) = 30t$.
Найдем конечное перемещение в момент времени $t_1 = 20$ с:
$s_1(20) = 30 \text{ м/с} \cdot 20 \text{ с} = 600$ м.
Для построения графика $s_1(t)$ необходимо соединить отрезком прямой две точки: начальную $(0 \text{ с}; 0 \text{ м})$ и конечную $(20 \text{ с}; 600 \text{ м})$.
Ответ: График зависимости перемещения от времени для первого случая представляет собой отрезок прямой, проведенный из начала координат $(0 \text{ с}, 0 \text{ м})$ в точку $(20 \text{ с}, 600 \text{ м})$.
2 Для второго тела скорость $v_2 = 20$ м/с. Уравнение движения имеет вид: $s_2(t) = 20t$.
Найдем конечное перемещение в момент времени $t_2 = 30$ с:
$s_2(30) = 20 \text{ м/с} \cdot 30 \text{ с} = 600$ м.
Для построения графика $s_2(t)$ необходимо соединить отрезком прямой две точки: начальную $(0 \text{ с}; 0 \text{ м})$ и конечную $(30 \text{ с}; 600 \text{ м})$.
Ответ: График зависимости перемещения от времени для второго случая представляет собой отрезок прямой, проведенный из начала координат $(0 \text{ с}, 0 \text{ м})$ в точку $(30 \text{ с}, 600 \text{ м})$.
3 Для третьего тела скорость $v_3 = 10$ м/с. Уравнение движения имеет вид: $s_3(t) = 10t$.
Найдем конечное перемещение в момент времени $t_3 = 60$ с:
$s_3(60) = 10 \text{ м/с} \cdot 60 \text{ с} = 600$ м.
Для построения графика $s_3(t)$ необходимо соединить отрезком прямой две точки: начальную $(0 \text{ с}; 0 \text{ м})$ и конечную $(60 \text{ с}; 600 \text{ м})$.
Ответ: График зависимости перемещения от времени для третьего случая представляет собой отрезок прямой, проведенный из начала координат $(0 \text{ с}, 0 \text{ м})$ в точку $(60 \text{ с}, 600 \text{ м})$.
Другие задания:
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ПрисоединитьсяМы подготовили для вас ответ c подробным объяснением домашего задания по физике за 8 класс, для упражнения номер 8.15 расположенного на странице 41 к задачнику серии сферы 2010 года издания для учащихся школ и гимназий.
Теперь на нашем сайте ГДЗ.ТОП вы всегда легко и бесплатно найдёте условие с правильным ответом на вопрос «Как решить ДЗ» и «Как сделать» задание по физике к упражнению №8.15 (с. 41), авторов: Артеменков (Денис Александрович), Ломаченков (Иван Алексеевич), Панебратцев (Юрий Анатольевич), учебного пособия издательства Просвещение.