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Номер 12, страница 35, часть 1 - гдз по физике 9 класс учебник Генденштейн, Булатова
Авторы: Генденштейн Л. Э., Булатова А. А., Корнильев И. Н., Кошкина А. В.
Тип: Учебник
Издательство: Бином
Год издания: 2016 - 2026
Часть: 1
Цвет обложки: бирюзовый
ISBN: 978-5-9963-3062-1
Популярные ГДЗ в 9 классе
Часть 1. Механические явления. Глава I. Кинематика. Параграф 3. Прямолинейное равноускоренное движение - номер 12, страница 35.
App\Models\Task {#1024 // resources/views/models/task/default.blade.php #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1433381 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "35" "field_page_end" => null "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/03-12" "field_display_title" => "12" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#331 #items: array:1 [ 0 => App\Models\Term {#1029 #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 {#1026 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#342 #items: array:1 [ 0 => App\Models\Branch {#1023 #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" => 1433206 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333 #items: array:1 [ 0 => App\Models\Term {#1033 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #original: array:7 [ "id" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #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_page_start" => "6" "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 {#1030 #items: array:1 [ 0 => App\Models\Book {#1032 #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" => 2980 "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 {#1034 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1036 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1038 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1040 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1045 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1046 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1048 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1050 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1052 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1053 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1055 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1056 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1057 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2016" "field_publication_year_until" => null "field_part" => "1, 2" "field_part_writing" => "Часть" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1111" "field_priority" => null "field_default_folder" => "/fizika_09/gendenshtejn-u/" "field_isbn" => "978-5-9963-3062-1" "field_cover" => array:2 [ …2] "field_cover_alts" => array:2 [ …2] "field_covers" => array:2 [ …2] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1059 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 2980 "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 {#1034 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1036 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1038 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1040 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1045 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1046 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1048 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1050 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1052 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1053 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1055 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1056 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1057 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2016" "field_publication_year_until" => null "field_part" => "1, 2" "field_part_writing" => "Часть" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1111" "field_priority" => null "field_default_folder" => "/fizika_09/gendenshtejn-u/" "field_isbn" => "978-5-9963-3062-1" "field_cover" => array:2 [ …2] "field_cover_alts" => array:2 [ …2] "field_covers" => array:2 [ …2] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1059 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #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 {#1064 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1433206 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333} "field_page_start" => "6" "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 {#1030} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1064} ] #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 {#1065 #items: array:4 [ 0 => App\Models\Branch {#1023} 1 => App\Models\Branch {#1066 #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" => 1433207 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механические явления" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1067 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "6" "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 {#1068 #items: array:1 [ 0 => App\Models\Book {#1069 #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" => 2980 "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 {#1070 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1072 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1074 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1076 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1081 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1082 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1084 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1086 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1088 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1089 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1090 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2016" "field_publication_year_until" => null "field_part" => "1, 2" "field_part_writing" => "Часть" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1111" "field_priority" => null "field_default_folder" => "/fizika_09/gendenshtejn-u/" "field_isbn" => "978-5-9963-3062-1" "field_cover" => array:2 [ …2] "field_cover_alts" => array:2 [ …2] "field_covers" => array:2 [ …2] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1095 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1096 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1097 …2} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1098 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 2980 "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 {#1070 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1072 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1074 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1076 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1081 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1082 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1084 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1086 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1088 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1089 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1090 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2016" "field_publication_year_until" => null "field_part" => "1, 2" "field_part_writing" => "Часть" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1111" "field_priority" => null "field_default_folder" => "/fizika_09/gendenshtejn-u/" "field_isbn" => "978-5-9963-3062-1" "field_cover" => array:2 [ …2] "field_cover_alts" => array:2 [ …2] "field_covers" => array:2 [ …2] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1095 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1096 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1097 …2} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1098 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #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 {#1100 #items: array:1 [ 0 => App\Models\Branch {#1101 #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" => 1433206 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1102 …2} "field_page_start" => "6" "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 {#1104 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1105 …2} ] #original: array:24 [ "id" => 1433206 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1102 …2} "field_page_start" => "6" "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 {#1104 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1105 …2} ] #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" => 1433207 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механические явления" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1067} "field_page_start" => "6" "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 {#1068} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1100} ] #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\Branch {#1106 #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" => 1433208 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Кинематика" "field_branch_order" => "I" "field_url" => null "field_branch_type" => 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:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => 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_page_start" => "6" "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 {#1109 #items: array:1 [ 0 => App\Models\Book {#1110 #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" => 2980 "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 {#1111 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1113 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1115 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1117 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1122 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1123 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1125 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1127 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1129 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1130 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1131 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1132 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1133 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1134 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2016" "field_publication_year_until" => null "field_part" => "1, 2" "field_part_writing" => "Часть" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1111" "field_priority" => null "field_default_folder" => "/fizika_09/gendenshtejn-u/" "field_isbn" => "978-5-9963-3062-1" "field_cover" => array:2 [ …2] "field_cover_alts" => array:2 [ …2] "field_covers" => array:2 [ …2] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1136 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1137 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1138 …2} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1139 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 2980 "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 {#1111 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1113 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1115 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1117 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1122 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1123 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1125 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1127 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1129 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1130 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1131 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1132 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1133 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1134 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2016" "field_publication_year_until" => null "field_part" => "1, 2" "field_part_writing" => "Часть" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1111" "field_priority" => null "field_default_folder" => "/fizika_09/gendenshtejn-u/" "field_isbn" => "978-5-9963-3062-1" "field_cover" => array:2 [ …2] "field_cover_alts" => array:2 [ …2] "field_covers" => array:2 [ …2] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1136 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1137 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1138 …2} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1139 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #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 {#1141 #items: array:1 [ 0 => App\Models\Branch {#1142 #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" => 1433207 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механические явления" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1143 …2} "field_page_start" => "6" "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 {#1144 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1145 …2} ] #original: array:24 [ "id" => 1433207 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механические явления" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1143 …2} "field_page_start" => "6" "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 {#1144 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1145 …2} ] #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" => 1433208 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Кинематика" "field_branch_order" => "I" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1107} "field_page_start" => "6" "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 {#1109} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1141} ] #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\Branch {#1182 #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" => 1433211 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Прямолинейное равноускоренное движение" "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1183 #items: array:1 [ 0 => App\Models\Term {#1184 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => "§" ] #original: array:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "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_page_start" => "30" "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 {#1185 #items: array:1 [ 0 => App\Models\Book {#1186 #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" => 2980 "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 {#1187 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1189 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1191 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1193 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1198 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1199 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1201 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1203 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1205 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1206 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1207 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1208 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1209 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1210 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2016" "field_publication_year_until" => null "field_part" => "1, 2" "field_part_writing" => "Часть" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1111" "field_priority" => null "field_default_folder" => "/fizika_09/gendenshtejn-u/" "field_isbn" => "978-5-9963-3062-1" "field_cover" => array:2 [ …2] "field_cover_alts" => array:2 [ …2] "field_covers" => array:2 [ …2] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1212 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1213 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1214 …2} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1215 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 2980 "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 {#1187 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1189 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1191 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1193 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1198 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1199 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1201 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1203 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1205 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1206 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1207 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1208 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1209 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1210 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2016" "field_publication_year_until" => null "field_part" => "1, 2" "field_part_writing" => "Часть" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1111" "field_priority" => null "field_default_folder" => "/fizika_09/gendenshtejn-u/" "field_isbn" => "978-5-9963-3062-1" "field_cover" => array:2 [ …2] "field_cover_alts" => array:2 [ …2] "field_covers" => array:2 [ …2] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1212 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1213 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1214 …2} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1215 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #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 {#1217 #items: array:1 [ 0 => App\Models\Branch {#1218 #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" => 1433208 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Кинематика" "field_branch_order" => "I" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1219 …2} "field_page_start" => "6" "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 {#1221 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1253 …2} ] #original: array:24 [ "id" => 1433208 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Кинематика" "field_branch_order" => "I" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1219 …2} "field_page_start" => "6" "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 {#1221 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1253 …2} ] #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" => 1433211 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Прямолинейное равноускоренное движение" "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1183} "field_page_start" => "30" "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 {#1185} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1217} ] #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 {#1294 #items: array:2 [ 0 => App\Models\Element {#1295 #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" => 1696122 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1296 #items: array:1 [ 0 => App\Models\Edition {#1297 #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" => 6168 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1298 …2} "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 {#1300 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1301 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1302 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6168 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1298 …2} "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 {#1300 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1301 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1302 …2} "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" => "1433381" "type" => "task" ] "text" => "<p><strong>12.</strong> Зависимость $v_x(t)$ для автомобиля, движущегося вдоль оси $\text{x}$, выражается формулой (в единицах СИ): $v_x = 10 + t$. Постройте график зависимости проекции скорости автомобиля от времени и определите, в какой момент скорость автомобиля станет равной 54 км/ч.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "12-1.jpg" "alt" => null "width" => "1573" "height" => 350 "path" => "/media/fizika_09/gendenshtejn-u/0-03/12-1.webp?ts=1759348149" ] ] ] #original: array:7 [ "id" => 1696122 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1296} "task" => array:2 [ "refs" => "1433381" "type" => "task" ] "text" => "<p><strong>12.</strong> Зависимость $v_x(t)$ для автомобиля, движущегося вдоль оси $\text{x}$, выражается формулой (в единицах СИ): $v_x = 10 + t$. Постройте график зависимости проекции скорости автомобиля от времени и определите, в какой момент скорость автомобиля станет равной 54 км/ч.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "12-1.jpg" "alt" => null "width" => "1573" "height" => 350 "path" => "/media/fizika_09/gendenshtejn-u/0-03/12-1.webp?ts=1759348149" ] ] ] #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 {#1303 #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" => 1780192 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1304 #items: array:1 [ 0 => App\Models\Edition {#1305 #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" => 6515 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1306 …2} "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 {#1308 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1309 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1310 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6515 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1306 …2} "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 {#1308 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1309 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1310 …2} "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" => "1433381" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Зависимость проекции скорости от времени: $v_x(t) = 10 + t$ (в СИ)</p><p>Конечная скорость автомобиля: $v_к = 54$ км/ч</p><p>Перевод в систему СИ:</p><p>$v_к = 54 \frac{\text{км}}{\text{ч}} = 54 \cdot \frac{1000 \text{ м}}{3600 \text{ с}} = \frac{540}{36} \text{ м/с} = 15 \text{ м/с}$</p><p><strong>Найти:</strong></p><p><strong>1.</strong> График зависимости $v_x(t)$.</p><p><strong>2.</strong> Момент времени $\text{t}$, когда скорость автомобиля станет равной $v_к$.</p><p><strong>Решение:</strong></p><p><strong>Построение графика зависимости проекции скорости автомобиля от времени</strong></p><p>Заданная зависимость проекции скорости от времени $v_x(t) = 10 + t$ является линейной функцией. В общем виде уравнение для равноускоренного движения записывается как $v_x(t) = v_{0x} + a_x t$. Сравнивая это уравнение с заданным, можно определить начальную скорость $v_{0x} = 10$ м/с и проекцию ускорения $a_x = 1$ м/с<sup>2</sup>.</p><p>Графиком линейной функции является прямая линия. Для ее построения в системе координат ($\text{t}$, $v_x$) найдем координаты двух точек:</p><p><strong>1.</strong> В начальный момент времени $t = 0$ с, проекция скорости равна $v_x = 10 + 0 = 10$ м/с. Координаты первой точки (0; 10).</p><p><strong>2.</strong> В произвольный момент времени, например $t = 5$ с, проекция скорости равна $v_x = 10 + 5 = 15$ м/с. Координаты второй точки (5; 15).</p><p>Проведя прямую через эти две точки, получим график зависимости $v_x(t)$. Это прямая, которая отсекает на оси скоростей отрезок, равный 10 м/с (начальная скорость), и имеет постоянный наклон к оси времени, тангенс которого равен ускорению.</p><p><strong>Определение момента времени, в который скорость автомобиля станет равной 54 км/ч</strong></p><p>Сначала необходимо перевести заданную скорость в единицы СИ (м/с), что уже было сделано в разделе "Дано": $v_к = 54$ км/ч = 15 м/с.</p><p>Движение автомобиля происходит вдоль оси $\text{x}$. Поскольку начальная скорость ($v_{0x} = 10$ м/с) и ускорение ($a_x = 1$ м/с<sup>2</sup>) положительны, скорость автомобиля будет постоянно возрастать, оставаясь положительной. Следовательно, модуль скорости $\text{v}$ равен ее проекции на ось $\text{x}$: $v = v_x$.</p><p>Подставим значение конечной скорости $v_x = 15$ м/с в уравнение движения:</p><p>$15 = 10 + t$</p><p>Решим это уравнение относительно времени $\text{t}$:</p><p>$t = 15 - 10$</p><p>$t = 5$ с</p><p><strong>Ответ:</strong> График зависимости проекции скорости от времени — это прямая линия, проходящая через точки (0; 10) и (5; 15). Скорость автомобиля станет равной 54 км/ч в момент времени $t = 5$ с.</p>" ] #original: array:6 [ "id" => 1780192 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1304} "task" => array:2 [ "refs" => "1433381" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Зависимость проекции скорости от времени: $v_x(t) = 10 + t$ (в СИ)</p><p>Конечная скорость автомобиля: $v_к = 54$ км/ч</p><p>Перевод в систему СИ:</p><p>$v_к = 54 \frac{\text{км}}{\text{ч}} = 54 \cdot \frac{1000 \text{ м}}{3600 \text{ с}} = \frac{540}{36} \text{ м/с} = 15 \text{ м/с}$</p><p><strong>Найти:</strong></p><p><strong>1.</strong> График зависимости $v_x(t)$.</p><p><strong>2.</strong> Момент времени $\text{t}$, когда скорость автомобиля станет равной $v_к$.</p><p><strong>Решение:</strong></p><p><strong>Построение графика зависимости проекции скорости автомобиля от времени</strong></p><p>Заданная зависимость проекции скорости от времени $v_x(t) = 10 + t$ является линейной функцией. В общем виде уравнение для равноускоренного движения записывается как $v_x(t) = v_{0x} + a_x t$. Сравнивая это уравнение с заданным, можно определить начальную скорость $v_{0x} = 10$ м/с и проекцию ускорения $a_x = 1$ м/с<sup>2</sup>.</p><p>Графиком линейной функции является прямая линия. Для ее построения в системе координат ($\text{t}$, $v_x$) найдем координаты двух точек:</p><p><strong>1.</strong> В начальный момент времени $t = 0$ с, проекция скорости равна $v_x = 10 + 0 = 10$ м/с. Координаты первой точки (0; 10).</p><p><strong>2.</strong> В произвольный момент времени, например $t = 5$ с, проекция скорости равна $v_x = 10 + 5 = 15$ м/с. Координаты второй точки (5; 15).</p><p>Проведя прямую через эти две точки, получим график зависимости $v_x(t)$. Это прямая, которая отсекает на оси скоростей отрезок, равный 10 м/с (начальная скорость), и имеет постоянный наклон к оси времени, тангенс которого равен ускорению.</p><p><strong>Определение момента времени, в который скорость автомобиля станет равной 54 км/ч</strong></p><p>Сначала необходимо перевести заданную скорость в единицы СИ (м/с), что уже было сделано в разделе "Дано": $v_к = 54$ км/ч = 15 м/с.</p><p>Движение автомобиля происходит вдоль оси $\text{x}$. Поскольку начальная скорость ($v_{0x} = 10$ м/с) и ускорение ($a_x = 1$ м/с<sup>2</sup>) положительны, скорость автомобиля будет постоянно возрастать, оставаясь положительной. Следовательно, модуль скорости $\text{v}$ равен ее проекции на ось $\text{x}$: $v = v_x$.</p><p>Подставим значение конечной скорости $v_x = 15$ м/с в уравнение движения:</p><p>$15 = 10 + t$</p><p>Решим это уравнение относительно времени $\text{t}$:</p><p>$t = 15 - 10$</p><p>$t = 5$ с</p><p><strong>Ответ:</strong> График зависимости проекции скорости от времени — это прямая линия, проходящая через точки (0; 10) и (5; 15). Скорость автомобиля станет равной 54 км/ч в момент времени $t = 5$ с.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1433382" "type" => "task" ] "previous" => array:2 [ "refs" => "1433380" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1311 #items: array:1 [ 0 => App\Models\Book {#1312 #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" => 2980 "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 {#1313 #items: array:1 [ 0 => App\Models\Term {#1314 #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 [ …6] "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 [ …6] "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 {#1315 #items: array:1 [ 0 => App\Models\Term {#1316 #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 [ …6] "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 [ …6] "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 {#1317 #items: array:1 [ 0 => App\Models\Term {#1318 #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" => 5208 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Бином" "field_cases" => null "field_translit" => "binom" ] #original: array:6 [ "id" => 5208 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Бином" "field_cases" => null "field_translit" => "binom" ] #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 {#1319 #items: array:4 [ 0 => App\Models\Term {#1320 #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" => 4104 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Генденштейн" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Лев" "field_patronymic" => "Элевич" "field_surname_rp" => "Генденштейна" ] #original: array:12 [ "id" => 4104 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Генденштейн" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Лев" "field_patronymic" => "Элевич" "field_surname_rp" => "Генденштейна" ] #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 {#1321 #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" => 3936 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Булатова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Альбина" "field_patronymic" => "Александрова" "field_surname_rp" => null ] #original: array:12 [ "id" => 3936 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Булатова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Альбина" "field_patronymic" => "Александрова" "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 {#1322 #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" => 4679 "created_at" => "2026-04-10 13:58:26" …10 ] #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] } 3 => App\Models\Term {#1323 #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 {#1324 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1325 #items: array:1 [ 0 => App\Models\Term {#1326 #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 {#1327 #items: array:1 [ 0 => App\Models\Term {#1328 #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 {#1329 #items: array:1 [ 0 => App\Models\Term {#1330 #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 {#1331 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1332 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1333 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1334 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1335 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1336 #items: array:1 [ 0 => App\Models\Term {#1337 #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_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2016" "field_publication_year_until" => null "field_part" => "1, 2" "field_part_writing" => "Часть" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1111" "field_priority" => null "field_default_folder" => "/fizika_09/gendenshtejn-u/" "field_isbn" => "978-5-9963-3062-1" "field_cover" => array:2 [ 0 => "/media/fizika_09/gendenshtejn-u/covers/cover1.webp?ts=1759256052" 1 => "/media/fizika_09/gendenshtejn-u/covers/cover2.webp?ts=1759256052" ] "field_cover_alts" => array:2 [ 0 => "" 1 => "" ] "field_covers" => array:2 [ 0 => array:4 [ "path" => "/media/fizika_09/gendenshtejn-u/covers/cover1.webp?ts=1759256052" "alt" => "" "width" => "1863" "height" => "2813" ] 1 => array:4 [ "path" => "/media/fizika_09/gendenshtejn-u/covers/cover2.webp?ts=1759256052" "alt" => "" "width" => "1863" "height" => "2809" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1338 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1339 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1340 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1341 #items: array:1 [ 0 => App\Models\Term {#1342 #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" => 2980 "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 {#1313} "field_class" => Illuminate\Database\Eloquent\Collection {#1315} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1317} "field_author" => Illuminate\Database\Eloquent\Collection {#1319} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1324} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1325} "field_country" => Illuminate\Database\Eloquent\Collection {#1327} "field_city" => Illuminate\Database\Eloquent\Collection {#1329} "field_series" => Illuminate\Database\Eloquent\Collection {#1331} "field_umk" => Illuminate\Database\Eloquent\Collection {#1332} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1333} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1334} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1335} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1336} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2016" "field_publication_year_until" => null "field_part" => "1, 2" "field_part_writing" => "Часть" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1111" "field_priority" => null "field_default_folder" => "/fizika_09/gendenshtejn-u/" "field_isbn" => "978-5-9963-3062-1" "field_cover" => array:2 [ 0 => "/media/fizika_09/gendenshtejn-u/covers/cover1.webp?ts=1759256052" 1 => "/media/fizika_09/gendenshtejn-u/covers/cover2.webp?ts=1759256052" ] "field_cover_alts" => array:2 [ 0 => "" 1 => "" ] "field_covers" => array:2 [ 0 => array:4 [ "path" => "/media/fizika_09/gendenshtejn-u/covers/cover1.webp?ts=1759256052" "alt" => "" "width" => "1863" "height" => "2813" ] 1 => array:4 [ "path" => "/media/fizika_09/gendenshtejn-u/covers/cover2.webp?ts=1759256052" "alt" => "" "width" => "1863" "height" => "2809" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1338} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1339} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1340} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1341} "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 } "page" => Illuminate\Database\Eloquent\Collection {#1357 #items: array:1 [ 0 => App\Models\BookPage {#1356 #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" => 1434676 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "35" "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/page-2-35" "field_display_title" => "35" "field_folder" => "2" "field_image_name" => "35" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1396 #items: array:1 [ 0 => App\Models\Branch {#1358 #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 [ …24] #original: array:24 [ …24] #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_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1428 #items: array:1 [ 0 => App\Models\Book {#1394 #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 [ …50] #original: array:50 [ …50] #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 "edition_groups" => Illuminate\Database\Eloquent\Collection {#1426 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1437 #items: array:1 [ 0 => App\Models\Element {#1436 #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 [ …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 } "next" => array:2 [ "refs" => "1434677" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1434675" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1429 #items: [] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1434676 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "35" "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/page-2-35" "field_display_title" => "35" "field_folder" => "2" "field_image_name" => "35" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1396} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1428} "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 {#1426} "content" => Illuminate\Database\Eloquent\Collection {#1437} "next" => array:2 [ "refs" => "1434677" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1434675" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1429} ] #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" => 1433381 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "35" "field_page_end" => null "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/03-12" "field_display_title" => "12" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#331} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1026} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#342} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1065} "content" => Illuminate\Database\Eloquent\Collection {#1294} "next" => array:2 [ "refs" => "1433382" "type" => "task" ] "previous" => array:2 [ "refs" => "1433380" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1311} "page" => array:2 [ "refs" => "1434676" "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 => "*" ] }
№12 (с. 35)
Условие. №12 (с. 35)
скриншот условия
12. Зависимость $v_x(t)$ для автомобиля, движущегося вдоль оси $\text{x}$, выражается формулой (в единицах СИ): $v_x = 10 + t$. Постройте график зависимости проекции скорости автомобиля от времени и определите, в какой момент скорость автомобиля станет равной 54 км/ч.
Решение. №12 (с. 35)
Дано:
Зависимость проекции скорости от времени: $v_x(t) = 10 + t$ (в СИ)
Конечная скорость автомобиля: $v_к = 54$ км/ч
Перевод в систему СИ:
$v_к = 54 \frac{\text{км}}{\text{ч}} = 54 \cdot \frac{1000 \text{ м}}{3600 \text{ с}} = \frac{540}{36} \text{ м/с} = 15 \text{ м/с}$
Найти:
1. График зависимости $v_x(t)$.
2. Момент времени $\text{t}$, когда скорость автомобиля станет равной $v_к$.
Решение:
Построение графика зависимости проекции скорости автомобиля от времени
Заданная зависимость проекции скорости от времени $v_x(t) = 10 + t$ является линейной функцией. В общем виде уравнение для равноускоренного движения записывается как $v_x(t) = v_{0x} + a_x t$. Сравнивая это уравнение с заданным, можно определить начальную скорость $v_{0x} = 10$ м/с и проекцию ускорения $a_x = 1$ м/с2.
Графиком линейной функции является прямая линия. Для ее построения в системе координат ($\text{t}$, $v_x$) найдем координаты двух точек:
1. В начальный момент времени $t = 0$ с, проекция скорости равна $v_x = 10 + 0 = 10$ м/с. Координаты первой точки (0; 10).
2. В произвольный момент времени, например $t = 5$ с, проекция скорости равна $v_x = 10 + 5 = 15$ м/с. Координаты второй точки (5; 15).
Проведя прямую через эти две точки, получим график зависимости $v_x(t)$. Это прямая, которая отсекает на оси скоростей отрезок, равный 10 м/с (начальная скорость), и имеет постоянный наклон к оси времени, тангенс которого равен ускорению.
Определение момента времени, в который скорость автомобиля станет равной 54 км/ч
Сначала необходимо перевести заданную скорость в единицы СИ (м/с), что уже было сделано в разделе "Дано": $v_к = 54$ км/ч = 15 м/с.
Движение автомобиля происходит вдоль оси $\text{x}$. Поскольку начальная скорость ($v_{0x} = 10$ м/с) и ускорение ($a_x = 1$ м/с2) положительны, скорость автомобиля будет постоянно возрастать, оставаясь положительной. Следовательно, модуль скорости $\text{v}$ равен ее проекции на ось $\text{x}$: $v = v_x$.
Подставим значение конечной скорости $v_x = 15$ м/с в уравнение движения:
$15 = 10 + t$
Решим это уравнение относительно времени $\text{t}$:
$t = 15 - 10$
$t = 5$ с
Ответ: График зависимости проекции скорости от времени — это прямая линия, проходящая через точки (0; 10) и (5; 15). Скорость автомобиля станет равной 54 км/ч в момент времени $t = 5$ с.
Другие задания:
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