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Номер 11, страница 21, 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 2. Прямолинейное равномерное движение - номер 11, страница 21.
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" => 1433326 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "21" "field_page_end" => null "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/02-11" "field_display_title" => "11" "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 {#1075 #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" => 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 {#1039 #items: array:1 [ 0 => App\Models\Term {#1038 #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 {#1040 #items: array:1 [ 0 => App\Models\Book {#1041 #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 {#1042 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1044 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1046 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1048 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1053 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1056 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1058 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1063 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1064 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1065 …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 {#1067 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1068 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1069 …2} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1070 …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 {#1042 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1044 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1046 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1048 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1053 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1056 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1058 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1063 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1064 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1065 …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 {#1067 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1068 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1069 …2} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1070 …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 {#1072 #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 {#1039} "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 {#1040} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1072} ] #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 {#1400 #items: array:4 [ 0 => App\Models\Branch {#1073 #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 {#1076 #items: array:1 [ 0 => App\Models\Term {#1074 #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 {#1077 #items: array:1 [ 0 => App\Models\Book {#1078 #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 {#1079 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1081 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1083 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1085 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1090 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1095 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1097 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1098 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1102 …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 {#1104 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1105 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1106 …2} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1107 …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 {#1079 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1081 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1083 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1085 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1090 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1095 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1097 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1098 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1102 …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 {#1104 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1105 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1106 …2} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1107 …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 {#1109 #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 {#1076} "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 {#1077} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1109} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Branch {#1110 #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 {#1111 #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 {#1112 #items: array:1 [ 0 => App\Models\Book {#1113 #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 {#1114 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1116 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1118 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1120 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1125 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1126 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1128 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1130 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1132 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1133 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1134 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1135 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1136 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1137 …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 {#1139 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1140 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1141 …2} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1142 …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 {#1114 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1116 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1118 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1120 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1125 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1126 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1128 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1130 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1132 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1133 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1134 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1135 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1136 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1137 …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 {#1139 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1140 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1141 …2} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1142 …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 {#1144 #items: array:1 [ 0 => App\Models\Branch {#1145 #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 {#1146 …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 {#1148 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1180 …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 {#1146 …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 {#1148 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1180 …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 {#1111} "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 {#1112} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1144} ] #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 {#1181 #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 {#1182 #items: array:1 [ 0 => App\Models\Term {#1183 #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 {#1184 #items: array:1 [ 0 => App\Models\Book {#1185 #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 {#1186 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1188 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1190 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1192 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1197 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1198 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1200 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1202 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1204 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1205 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1206 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1207 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1208 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1209 …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 {#1211 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1212 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1213 …2} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1214 …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 {#1186 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1188 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1190 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1192 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1197 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1198 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1200 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1202 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1204 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1205 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1206 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1207 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1208 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1209 …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 {#1211 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1212 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1213 …2} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1214 …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 {#1216 #items: array:1 [ 0 => App\Models\Branch {#1217 #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 {#1218 …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 {#1219 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1251 …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 {#1218 …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 {#1219 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1251 …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 {#1182} "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 {#1184} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1216} ] #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 {#1288 #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" => 1433210 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Прямолинейное равномерное движение" "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1289 #items: array:1 [ 0 => App\Models\Term {#1290 #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" => "18" "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 {#1291 #items: array:1 [ 0 => App\Models\Book {#1292 #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 {#1293 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1295 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1297 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1299 …2} …41 ] #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 } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1323 #items: array:1 [ 0 => App\Models\Branch {#1324 #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 } ] #original: array:24 [ "id" => 1433210 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Прямолинейное равномерное движение" "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1289} "field_page_start" => "18" "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 {#1291} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1323} ] #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 {#1401 #items: array:2 [ 0 => App\Models\Element {#1411 #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" => 1696067 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1420 #items: array:1 [ 0 => App\Models\Edition {#1412 #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 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1433326" "type" => "task" ] "text" => "<p><strong>11.</strong> Зависимость координаты $\text{x}$ от времени для двух тел, движущихся вдоль оси $\text{x}$, выражается в единицах СИ формулами $x_1 = 6 - 5t$; $x_2 = -10 + 3t$.</p><p><strong>а)</strong> Начертите в тетради на одном чертеже графики зависимости $x_1(t)$ и $x_2(t)$.</p><p><strong>б)</strong> Что обозначает точка пересечения графиков?</p><p><strong>в)</strong> Найдите графически (то есть с использованием графика), чему равны координата и время встречи тел в единицах СИ.</p><p><strong>г)</strong> Проверьте правильность выполнения предыдущего задания, найдя момент встречи тел $t_в$ из условия $x_1(t_в) = x_2(t_в)$. Определив момент встречи, найдите аналитически (то есть с помощью формул) координату встречи тел.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "11-1.jpg" "alt" => null "width" => "1534" "height" => 821 "path" => "/media/fizika_09/gendenshtejn-u/0-02/11-1.webp?ts=1759348132" ] ] ] #original: array:7 [ "id" => 1696067 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1420} "task" => array:2 [ "refs" => "1433326" "type" => "task" ] "text" => "<p><strong>11.</strong> Зависимость координаты $\text{x}$ от времени для двух тел, движущихся вдоль оси $\text{x}$, выражается в единицах СИ формулами $x_1 = 6 - 5t$; $x_2 = -10 + 3t$.</p><p><strong>а)</strong> Начертите в тетради на одном чертеже графики зависимости $x_1(t)$ и $x_2(t)$.</p><p><strong>б)</strong> Что обозначает точка пересечения графиков?</p><p><strong>в)</strong> Найдите графически (то есть с использованием графика), чему равны координата и время встречи тел в единицах СИ.</p><p><strong>г)</strong> Проверьте правильность выполнения предыдущего задания, найдя момент встречи тел $t_в$ из условия $x_1(t_в) = x_2(t_в)$. Определив момент встречи, найдите аналитически (то есть с помощью формул) координату встречи тел.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "11-1.jpg" "alt" => null "width" => "1534" "height" => 821 "path" => "/media/fizika_09/gendenshtejn-u/0-02/11-1.webp?ts=1759348132" ] ] ] #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 {#1418 #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" => 1780137 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1428 #items: array:1 [ 0 => App\Models\Edition {#1419 #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 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1433326" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Зависимость координаты от времени для первого тела: $x_1 = 6 - 5t$.</p><p>Зависимость координаты от времени для второго тела: $x_2 = -10 + 3t$.</p><p>Все величины выражены в единицах СИ, то есть координата $\text{x}$ в метрах (м), а время $\text{t}$ в секундах (с).</p><p><strong>Найти:</strong></p><p>а) Начертить графики зависимостей $x_1(t)$ и $x_2(t)$.</p><p>б) Объяснить, что обозначает точка пересечения графиков.</p><p>в) Найти координату и время встречи тел графически.</p><p>г) Найти координату и время встречи тел аналитически и проверить результат.</p><p><strong>Решение:</strong></p><p><strong>а) Начертите в тетради на одном чертеже графики зависимости $x_1(t)$ и $x_2(t)$.</strong></p><p>Обе зависимости, $x_1(t)$ и $x_2(t)$, являются линейными функциями вида $x = x_0 + v_x t$. Графиками таких функций являются прямые линии. Для построения прямой достаточно двух точек.</p><p>Для графика $x_1(t) = 6 - 5t$:</p><p><strong>1.</strong> Найдем начальную координату при $t = 0$ с: $x_1(0) = 6 - 5 \cdot 0 = 6$ м. Получаем точку (0; 6).</p><p><strong>2.</strong> Найдем координату в другой момент времени, например, при $t = 2$ с: $x_1(2) = 6 - 5 \cdot 2 = 6 - 10 = -4$ м. Получаем точку (2; -4).</p><p>Проведем прямую через точки (0; 6) и (2; -4) на координатной плоскости $x(t)$.</p><p>Для графика $x_2(t) = -10 + 3t$:</p><p><strong>1.</strong> Найдем начальную координату при $t = 0$ с: $x_2(0) = -10 + 3 \cdot 0 = -10$ м. Получаем точку (0; -10).</p><p><strong>2.</strong> Найдем координату в другой момент времени, например, при $t = 2$ с: $x_2(2) = -10 + 3 \cdot 2 = -10 + 6 = -4$ м. Получаем точку (2; -4).</p><p>Проведем прямую через точки (0; -10) и (2; -4) на той же координатной плоскости.</p><p><strong>Ответ:</strong> На чертеже должны быть построены две прямые линии, проходящие через указанные точки. Ось абсцисс — время $\text{t}$ (в с), ось ординат — координата $\text{x}$ (в м). Графики пересекаются в одной точке.</p><p><strong>б) Что обозначает точка пересечения графиков?</strong></p><p>Точка пересечения графиков зависимостей координаты от времени $x(t)$ для двух тел показывает момент времени и координату, в которые тела встретились. В этой точке время и координата у обоих тел совпадают, то есть $t_1 = t_2$ и $x_1 = x_2$.</p><p><strong>Ответ:</strong> Точка пересечения графиков обозначает место и время встречи тел.</p><p><strong>в) Найдите графически (то есть с использованием графика), чему равны координата и время встречи тел в единицах СИ.</strong></p><p>Построив графики, как описано в пункте (а), находим на чертеже точку их пересечения. Проекции этой точки на оси координат дают нам искомые значения времени и координаты встречи.</p><p>Из построения видно, что графики пересекаются в точке с координатами (2; -4).</p><p>Следовательно, время встречи $t_в = 2$ с, а координата встречи $x_в = -4$ м.</p><p><strong>Ответ:</strong> Время встречи $t_в = 2$ с, координата встречи $x_в = -4$ м.</p><p><strong>г) Проверьте правильность выполнения предыдущего задания, найдя момент встречи тел $t_в$ из условия $x_1(t_в) = x_2(t_в)$. Определив момент встречи, найдите аналитически (то есть с помощью формул) координату встречи тел.</strong></p><p>В момент встречи $t_в$ координаты тел равны: $x_1(t_в) = x_2(t_в)$. Приравняем правые части уравнений движения:</p><p>$6 - 5t_в = -10 + 3t_в$</p><p>Перенесем слагаемые с $t_в$ в одну сторону, а свободные члены — в другую:</p><p>$6 + 10 = 3t_в + 5t_в$</p><p>$16 = 8t_в$</p><p>Отсюда находим время встречи:</p><p>$t_в = \frac{16}{8} = 2$ с.</p><p>Теперь подставим найденное время в любое из уравнений движения, чтобы найти координату встречи $x_в$.</p><p>Используя первое уравнение:</p><p>$x_в = x_1(2) = 6 - 5 \cdot 2 = 6 - 10 = -4$ м.</p><p>Для проверки подставим во второе уравнение:</p><p>$x_в = x_2(2) = -10 + 3 \cdot 2 = -10 + 6 = -4$ м.</p><p>Результаты совпадают. Аналитический расчет подтверждает значения, найденные графически.</p><p><strong>Ответ:</strong> Время встречи $t_в = 2$ с, координата встречи $x_в = -4$ м. Результаты, полученные аналитически, совпадают с результатами, полученными графически.</p>" ] #original: array:6 [ "id" => 1780137 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1428} "task" => array:2 [ "refs" => "1433326" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Зависимость координаты от времени для первого тела: $x_1 = 6 - 5t$.</p><p>Зависимость координаты от времени для второго тела: $x_2 = -10 + 3t$.</p><p>Все величины выражены в единицах СИ, то есть координата $\text{x}$ в метрах (м), а время $\text{t}$ в секундах (с).</p><p><strong>Найти:</strong></p><p>а) Начертить графики зависимостей $x_1(t)$ и $x_2(t)$.</p><p>б) Объяснить, что обозначает точка пересечения графиков.</p><p>в) Найти координату и время встречи тел графически.</p><p>г) Найти координату и время встречи тел аналитически и проверить результат.</p><p><strong>Решение:</strong></p><p><strong>а) Начертите в тетради на одном чертеже графики зависимости $x_1(t)$ и $x_2(t)$.</strong></p><p>Обе зависимости, $x_1(t)$ и $x_2(t)$, являются линейными функциями вида $x = x_0 + v_x t$. Графиками таких функций являются прямые линии. Для построения прямой достаточно двух точек.</p><p>Для графика $x_1(t) = 6 - 5t$:</p><p><strong>1.</strong> Найдем начальную координату при $t = 0$ с: $x_1(0) = 6 - 5 \cdot 0 = 6$ м. Получаем точку (0; 6).</p><p><strong>2.</strong> Найдем координату в другой момент времени, например, при $t = 2$ с: $x_1(2) = 6 - 5 \cdot 2 = 6 - 10 = -4$ м. Получаем точку (2; -4).</p><p>Проведем прямую через точки (0; 6) и (2; -4) на координатной плоскости $x(t)$.</p><p>Для графика $x_2(t) = -10 + 3t$:</p><p><strong>1.</strong> Найдем начальную координату при $t = 0$ с: $x_2(0) = -10 + 3 \cdot 0 = -10$ м. Получаем точку (0; -10).</p><p><strong>2.</strong> Найдем координату в другой момент времени, например, при $t = 2$ с: $x_2(2) = -10 + 3 \cdot 2 = -10 + 6 = -4$ м. Получаем точку (2; -4).</p><p>Проведем прямую через точки (0; -10) и (2; -4) на той же координатной плоскости.</p><p><strong>Ответ:</strong> На чертеже должны быть построены две прямые линии, проходящие через указанные точки. Ось абсцисс — время $\text{t}$ (в с), ось ординат — координата $\text{x}$ (в м). Графики пересекаются в одной точке.</p><p><strong>б) Что обозначает точка пересечения графиков?</strong></p><p>Точка пересечения графиков зависимостей координаты от времени $x(t)$ для двух тел показывает момент времени и координату, в которые тела встретились. В этой точке время и координата у обоих тел совпадают, то есть $t_1 = t_2$ и $x_1 = x_2$.</p><p><strong>Ответ:</strong> Точка пересечения графиков обозначает место и время встречи тел.</p><p><strong>в) Найдите графически (то есть с использованием графика), чему равны координата и время встречи тел в единицах СИ.</strong></p><p>Построив графики, как описано в пункте (а), находим на чертеже точку их пересечения. Проекции этой точки на оси координат дают нам искомые значения времени и координаты встречи.</p><p>Из построения видно, что графики пересекаются в точке с координатами (2; -4).</p><p>Следовательно, время встречи $t_в = 2$ с, а координата встречи $x_в = -4$ м.</p><p><strong>Ответ:</strong> Время встречи $t_в = 2$ с, координата встречи $x_в = -4$ м.</p><p><strong>г) Проверьте правильность выполнения предыдущего задания, найдя момент встречи тел $t_в$ из условия $x_1(t_в) = x_2(t_в)$. Определив момент встречи, найдите аналитически (то есть с помощью формул) координату встречи тел.</strong></p><p>В момент встречи $t_в$ координаты тел равны: $x_1(t_в) = x_2(t_в)$. Приравняем правые части уравнений движения:</p><p>$6 - 5t_в = -10 + 3t_в$</p><p>Перенесем слагаемые с $t_в$ в одну сторону, а свободные члены — в другую:</p><p>$6 + 10 = 3t_в + 5t_в$</p><p>$16 = 8t_в$</p><p>Отсюда находим время встречи:</p><p>$t_в = \frac{16}{8} = 2$ с.</p><p>Теперь подставим найденное время в любое из уравнений движения, чтобы найти координату встречи $x_в$.</p><p>Используя первое уравнение:</p><p>$x_в = x_1(2) = 6 - 5 \cdot 2 = 6 - 10 = -4$ м.</p><p>Для проверки подставим во второе уравнение:</p><p>$x_в = x_2(2) = -10 + 3 \cdot 2 = -10 + 6 = -4$ м.</p><p>Результаты совпадают. Аналитический расчет подтверждает значения, найденные графически.</p><p><strong>Ответ:</strong> Время встречи $t_в = 2$ с, координата встречи $x_в = -4$ м. Результаты, полученные аналитически, совпадают с результатами, полученными графически.</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" => "1433327" "type" => "task" ] "previous" => array:2 [ "refs" => "1433325" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1452 #items: array:1 [ 0 => App\Models\Book {#1408 #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 {#1402 #items: array:1 [ 0 => App\Models\Term {#1403 #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 {#1410 #items: array:1 [ 0 => App\Models\Term {#1406 #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 {#1404 #items: array:1 [ 0 => App\Models\Term {#1407 #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 {#1405 #items: array:4 [ 0 => App\Models\Term {#1426 #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 {#1427 #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 {#1429 #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] } 3 => App\Models\Term {#1430 #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 {#1431 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1432 #items: array:1 [ 0 => App\Models\Term {#1433 #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 {#1434 #items: array:1 [ 0 => App\Models\Term {#1435 #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 {#1436 #items: array:1 [ 0 => App\Models\Term {#1437 #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 {#1438 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1439 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1440 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1441 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1442 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1443 #items: array:1 [ 0 => App\Models\Term {#1444 #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 {#1445 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1446 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1447 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1448 #items: array:1 [ 0 => App\Models\Term {#1449 #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 {#1402} "field_class" => Illuminate\Database\Eloquent\Collection {#1410} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1404} "field_author" => Illuminate\Database\Eloquent\Collection {#1405} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1431} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1432} "field_country" => Illuminate\Database\Eloquent\Collection {#1434} "field_city" => Illuminate\Database\Eloquent\Collection {#1436} "field_series" => Illuminate\Database\Eloquent\Collection {#1438} "field_umk" => Illuminate\Database\Eloquent\Collection {#1439} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1440} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1441} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1442} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1443} "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 {#1445} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1446} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1447} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1448} "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 {#1457 #items: array:1 [ 0 => App\Models\BookPage {#1456 #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" => 1434662 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "21" "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/page-2-21" "field_display_title" => "21" "field_folder" => "2" "field_image_name" => "21" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1496 #items: array:1 [ 0 => App\Models\Branch {#1458 #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 {#1494 #items: array:1 [ 0 => App\Models\Book {#1408} ] #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 {#1495 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1506 #items: array:1 [ 0 => App\Models\Element {#1505 #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" => "1434663" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1434661" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1497 #items: array:3 [ 0 => App\Models\Task {#1512 #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 [ …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] } 1 => App\Models\Task {#1551 #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 [ …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] } 2 => App\Models\Task {#1541 #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 [ …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 } ] #original: array:21 [ "id" => 1434662 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "21" "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/page-2-21" "field_display_title" => "21" "field_folder" => "2" "field_image_name" => "21" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1496} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1494} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null 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№11 (с. 21)
Условие. №11 (с. 21)
скриншот условия
11. Зависимость координаты $\text{x}$ от времени для двух тел, движущихся вдоль оси $\text{x}$, выражается в единицах СИ формулами $x_1 = 6 - 5t$; $x_2 = -10 + 3t$.
а) Начертите в тетради на одном чертеже графики зависимости $x_1(t)$ и $x_2(t)$.
б) Что обозначает точка пересечения графиков?
в) Найдите графически (то есть с использованием графика), чему равны координата и время встречи тел в единицах СИ.
г) Проверьте правильность выполнения предыдущего задания, найдя момент встречи тел $t_в$ из условия $x_1(t_в) = x_2(t_в)$. Определив момент встречи, найдите аналитически (то есть с помощью формул) координату встречи тел.
Решение. №11 (с. 21)
Дано:
Зависимость координаты от времени для первого тела: $x_1 = 6 - 5t$.
Зависимость координаты от времени для второго тела: $x_2 = -10 + 3t$.
Все величины выражены в единицах СИ, то есть координата $\text{x}$ в метрах (м), а время $\text{t}$ в секундах (с).
Найти:
а) Начертить графики зависимостей $x_1(t)$ и $x_2(t)$.
б) Объяснить, что обозначает точка пересечения графиков.
в) Найти координату и время встречи тел графически.
г) Найти координату и время встречи тел аналитически и проверить результат.
Решение:
а) Начертите в тетради на одном чертеже графики зависимости $x_1(t)$ и $x_2(t)$.
Обе зависимости, $x_1(t)$ и $x_2(t)$, являются линейными функциями вида $x = x_0 + v_x t$. Графиками таких функций являются прямые линии. Для построения прямой достаточно двух точек.
Для графика $x_1(t) = 6 - 5t$:
1. Найдем начальную координату при $t = 0$ с: $x_1(0) = 6 - 5 \cdot 0 = 6$ м. Получаем точку (0; 6).
2. Найдем координату в другой момент времени, например, при $t = 2$ с: $x_1(2) = 6 - 5 \cdot 2 = 6 - 10 = -4$ м. Получаем точку (2; -4).
Проведем прямую через точки (0; 6) и (2; -4) на координатной плоскости $x(t)$.
Для графика $x_2(t) = -10 + 3t$:
1. Найдем начальную координату при $t = 0$ с: $x_2(0) = -10 + 3 \cdot 0 = -10$ м. Получаем точку (0; -10).
2. Найдем координату в другой момент времени, например, при $t = 2$ с: $x_2(2) = -10 + 3 \cdot 2 = -10 + 6 = -4$ м. Получаем точку (2; -4).
Проведем прямую через точки (0; -10) и (2; -4) на той же координатной плоскости.
Ответ: На чертеже должны быть построены две прямые линии, проходящие через указанные точки. Ось абсцисс — время $\text{t}$ (в с), ось ординат — координата $\text{x}$ (в м). Графики пересекаются в одной точке.
б) Что обозначает точка пересечения графиков?
Точка пересечения графиков зависимостей координаты от времени $x(t)$ для двух тел показывает момент времени и координату, в которые тела встретились. В этой точке время и координата у обоих тел совпадают, то есть $t_1 = t_2$ и $x_1 = x_2$.
Ответ: Точка пересечения графиков обозначает место и время встречи тел.
в) Найдите графически (то есть с использованием графика), чему равны координата и время встречи тел в единицах СИ.
Построив графики, как описано в пункте (а), находим на чертеже точку их пересечения. Проекции этой точки на оси координат дают нам искомые значения времени и координаты встречи.
Из построения видно, что графики пересекаются в точке с координатами (2; -4).
Следовательно, время встречи $t_в = 2$ с, а координата встречи $x_в = -4$ м.
Ответ: Время встречи $t_в = 2$ с, координата встречи $x_в = -4$ м.
г) Проверьте правильность выполнения предыдущего задания, найдя момент встречи тел $t_в$ из условия $x_1(t_в) = x_2(t_в)$. Определив момент встречи, найдите аналитически (то есть с помощью формул) координату встречи тел.
В момент встречи $t_в$ координаты тел равны: $x_1(t_в) = x_2(t_в)$. Приравняем правые части уравнений движения:
$6 - 5t_в = -10 + 3t_в$
Перенесем слагаемые с $t_в$ в одну сторону, а свободные члены — в другую:
$6 + 10 = 3t_в + 5t_в$
$16 = 8t_в$
Отсюда находим время встречи:
$t_в = \frac{16}{8} = 2$ с.
Теперь подставим найденное время в любое из уравнений движения, чтобы найти координату встречи $x_в$.
Используя первое уравнение:
$x_в = x_1(2) = 6 - 5 \cdot 2 = 6 - 10 = -4$ м.
Для проверки подставим во второе уравнение:
$x_в = x_2(2) = -10 + 3 \cdot 2 = -10 + 6 = -4$ м.
Результаты совпадают. Аналитический расчет подтверждает значения, найденные графически.
Ответ: Время встречи $t_в = 2$ с, координата встречи $x_в = -4$ м. Результаты, полученные аналитически, совпадают с результатами, полученными графически.
Другие задания:
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