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Номер 2, страница 8, часть 1 - гдз по физике 9 класс рабочая тетрадь Грачев, Погожев
Авторы: Грачев А. В., Погожев В. А., Боков П. Ю., Вишнякова Е. А.
Тип: рабочая тетрадь
Издательство: Просвещение
Год издания: 2021 - 2026
Часть: 1
Цвет обложки: синий
ISBN: 978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)
Популярные ГДЗ в 9 классе
Часть 1. Глава 1. Кинематика. Параграф 2. Прямолинейное движение - номер 2, страница 8.
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" => 1434890 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "8" "field_page_end" => "9" "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/02-2" "field_display_title" => "2" "field_outside_task" => "0" "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 {#1076 #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" => 1434806 "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" => "4" "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" => 1203 "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" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "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" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ …3] "field_cover_alts" => array:3 [ …3] "field_covers" => array:3 [ …3] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1068 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1069 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1070 …2} "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1071 …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" => 1203 "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" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "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" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ …3] "field_cover_alts" => array:3 [ …3] "field_covers" => array:3 [ …3] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1068 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1069 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1070 …2} "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1071 …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 {#1073 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434806 "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" => "4" "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 {#1073} ] #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 {#1234 #items: array:3 [ 0 => App\Models\Branch {#1074 #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" => 1434806 "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 {#1077 #items: array:1 [ 0 => App\Models\Term {#1075 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array: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" => "4" "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 {#1078 #items: array:1 [ 0 => App\Models\Book {#1079 #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" => 1203 "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 {#1080 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1082 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1084 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1086 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1096 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1098 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1103 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1105 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "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" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ …3] "field_cover_alts" => array:3 [ …3] "field_covers" => array:3 [ …3] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1106 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1107 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1108 …2} "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1109 …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" => 1203 "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 {#1080 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1082 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1084 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1086 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1096 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1098 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1103 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1105 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "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" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ …3] "field_cover_alts" => array:3 [ …3] "field_covers" => array:3 [ …3] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1106 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1107 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1108 …2} "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1109 …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 {#1111 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434806 "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 {#1077} "field_page_start" => "4" "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 {#1078} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1111} ] #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 {#1112 #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" => 1434807 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Кинематика" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1113 #items: array:1 [ 0 => App\Models\Term {#1114 #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" => "4" "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 {#1115 #items: array:1 [ 0 => App\Models\Book {#1116 #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" => 1203 "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 {#1117 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1119 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1121 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1123 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1128 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1129 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1131 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1133 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1135 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1136 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1137 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1138 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1140 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1142 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "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" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ …3] "field_cover_alts" => array:3 [ …3] "field_covers" => array:3 [ …3] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1143 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1144 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1145 …2} "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1146 …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" => 1203 "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 {#1117 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1119 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1121 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1123 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1128 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1129 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1131 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1133 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1135 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1136 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1137 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1138 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1140 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1142 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "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" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ …3] "field_cover_alts" => array:3 [ …3] "field_covers" => array:3 [ …3] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1143 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1144 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1145 …2} "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1146 …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 {#1148 #items: array:1 [ 0 => App\Models\Branch {#1149 #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" => 1434806 "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 {#1150 …2} "field_page_start" => "4" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1152 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1153 …2} ] #original: array:24 [ "id" => 1434806 "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 {#1150 …2} "field_page_start" => "4" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1152 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1153 …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" => 1434807 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Кинематика" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1113} "field_page_start" => "4" "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 {#1115} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1148} ] #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 {#1154 #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" => 1434810 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Прямолинейное движение" "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1155 #items: array:1 [ 0 => App\Models\Term {#1156 #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" => "8" "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 {#1157 #items: array:1 [ 0 => App\Models\Book {#1158 #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" => 1203 "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 {#1159 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1161 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1163 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1165 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1170 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1171 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1173 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1175 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1177 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1178 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1179 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1180 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1182 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1184 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "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" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ …3] "field_cover_alts" => array:3 [ …3] "field_covers" => array:3 [ …3] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1185 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1186 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1187 …2} "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1188 …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" => 1203 "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 {#1159 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1161 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1163 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1165 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1170 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1171 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1173 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1175 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1177 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1178 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1179 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1180 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1182 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1184 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "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" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ …3] "field_cover_alts" => array:3 [ …3] "field_covers" => array:3 [ …3] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1185 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1186 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1187 …2} "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1188 …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 {#1190 #items: array:1 [ 0 => App\Models\Branch {#1191 #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" => 1434807 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Кинематика" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1192 …2} "field_page_start" => "4" "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 {#1194 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1195 …2} ] #original: array:24 [ "id" => 1434807 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Кинематика" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1192 …2} "field_page_start" => "4" "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 {#1194 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1195 …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" => 1434810 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Прямолинейное движение" "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1155} "field_page_start" => "8" "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 {#1157} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1190} ] #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 {#1233 #items: array:2 [ 0 => App\Models\Element {#1244 #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" => 1698278 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1253 #items: array:1 [ 0 => App\Models\Edition {#1245 #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" => 6173 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1247 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1248 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1249 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1250 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6173 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1247 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1248 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1249 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1250 …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" => "1434890" "type" => "task" ] "text" => "<p><strong>2.</strong> В таблице приведены законы движения тел вдоль оси $\text{X}$, в которых координату $\text{x}$ измеряют в метрах, а время $\text{t}$ – в секундах. Заполните таблицу.</p><p><strong>Закон движения</strong></p><p><strong>Начальная координата</strong></p><p><strong>Значение</strong></p><p><strong>начальной скорости</strong></p><p><strong>начального ускорения</strong></p><p><strong>Координата $\text{x}$ в момент времени</strong></p><p><strong>1 </strong>с</p><p><strong>3 </strong>с</p><p><strong>5 </strong>с</p><p><strong>Момент времени, когда координата $\text{x}$ тела равна</strong></p><p>$x(t) = 5t$</p><p>5 м</p><p><em>Окончание</em></p><p><strong>Закон движения</strong></p><p><strong>Начальная координата</strong></p><p><strong>Значение</strong></p><p><strong>начальной скорости</strong></p><p><strong>начального ускорения</strong></p><p><strong>Координата $\text{x}$ в момент времени</strong></p><p><strong>1 </strong>с</p><p><strong>3 </strong>с</p><p><strong>5 </strong>с</p><p><strong>Момент времени, когда координата $\text{x}$ тела равна</strong></p><p>$x(t) = 5t$</p><p>10 м</p><p>20 м</p><p>10 м</p><p>$x(t) = -5 + 15t$</p><p>25 м</p><p>55 м</p><p>50 м</p><p>$x(t) = 50 + 2t - 2,5t^2$</p><p>44 м</p><p>18 м</p>" "img" => array:2 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "1953" "height" => 705 "path" => "/media/fizika_09/grachev-rt/0-02/2-1.webp?ts=1759402618" ] 1 => array:5 [ "name" => "2-2.jpg" "alt" => null "width" => "1940" "height" => 1177 "path" => "/media/fizika_09/grachev-rt/0-02/2-2.webp?ts=1759402618" ] ] ] #original: array:7 [ "id" => 1698278 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1253} "task" => array:2 [ "refs" => "1434890" "type" => "task" ] "text" => "<p><strong>2.</strong> В таблице приведены законы движения тел вдоль оси $\text{X}$, в которых координату $\text{x}$ измеряют в метрах, а время $\text{t}$ – в секундах. Заполните таблицу.</p><p><strong>Закон движения</strong></p><p><strong>Начальная координата</strong></p><p><strong>Значение</strong></p><p><strong>начальной скорости</strong></p><p><strong>начального ускорения</strong></p><p><strong>Координата $\text{x}$ в момент времени</strong></p><p><strong>1 </strong>с</p><p><strong>3 </strong>с</p><p><strong>5 </strong>с</p><p><strong>Момент времени, когда координата $\text{x}$ тела равна</strong></p><p>$x(t) = 5t$</p><p>5 м</p><p><em>Окончание</em></p><p><strong>Закон движения</strong></p><p><strong>Начальная координата</strong></p><p><strong>Значение</strong></p><p><strong>начальной скорости</strong></p><p><strong>начального ускорения</strong></p><p><strong>Координата $\text{x}$ в момент времени</strong></p><p><strong>1 </strong>с</p><p><strong>3 </strong>с</p><p><strong>5 </strong>с</p><p><strong>Момент времени, когда координата $\text{x}$ тела равна</strong></p><p>$x(t) = 5t$</p><p>10 м</p><p>20 м</p><p>10 м</p><p>$x(t) = -5 + 15t$</p><p>25 м</p><p>55 м</p><p>50 м</p><p>$x(t) = 50 + 2t - 2,5t^2$</p><p>44 м</p><p>18 м</p>" "img" => array:2 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "1953" "height" => 705 "path" => "/media/fizika_09/grachev-rt/0-02/2-1.webp?ts=1759402618" ] 1 => array:5 [ "name" => "2-2.jpg" "alt" => null "width" => "1940" "height" => 1177 "path" => "/media/fizika_09/grachev-rt/0-02/2-2.webp?ts=1759402618" ] ] ] #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 {#1251 #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" => 1734264 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1261 #items: array:1 [ 0 => App\Models\Edition {#1252 #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" => 6327 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1255 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1256 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1257 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1258 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6327 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1255 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1256 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1257 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1258 …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" => "1434890" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Законы движения трех тел:</p><p>1. $x(t) = 5t$</p><p>2. $x(t) = -5 + 15t$</p><p>3. $x(t) = 50 + 2t - 2.5t^2$</p><p>Координата $x$ измеряется в метрах (м), время $t$ – в секундах (с). Все величины представлены в системе СИ, перевод не требуется.</p><p><strong>Найти:</strong></p><p>Для каждого закона движения определить:</p><p>1. Начальную координату ($x_0$).</p><p>2. Значение начальной скорости ($v_0$).</p><p>3. Значение начального ускорения ($a$).</p><p>4. Координату $x$ в моменты времени $t=1$ с, $t=3$ с, $t=5$ с.</p><p>5. Момент времени $t$, когда координата $x$ тела принимает заданные значения.</p><p><strong>Решение:</strong></p><p>Общий вид закона равноускоренного прямолинейного движения вдоль оси X: $x(t) = x_0 + v_0 t + \frac{a t^2}{2}$.</p><p>Будем сравнивать каждый заданный закон движения с этой общей формулой и выполнять необходимые расчеты для заполнения таблицы.</p><p><strong>Для закона движения $x(t) = 5t$</strong></p><p><strong>Начальная координата</strong></p><p>Сравниваем уравнение $x(t) = 5t$ с общей формулой. Свободный член, соответствующий начальной координате $x_0$, отсутствует, следовательно, он равен нулю.</p><p><strong>Ответ:</strong> $x_0 = 0$ м.</p><p><strong>Значение начальной скорости</strong></p><p>Коэффициент при $t$ в первой степени соответствует начальной скорости $v_0$ и равен 5.</p><p><strong>Ответ:</strong> $v_0 = 5$ м/с.</p><p><strong>Значение начального ускорения</strong></p><p>Слагаемое с $t^2$ отсутствует, значит, коэффициент при нем $\frac{a}{2}$ равен нулю, следовательно, ускорение $a=0$. Движение является равномерным прямолинейным.</p><p><strong>Ответ:</strong> $a = 0$ м/с².</p><p><strong>Координата $x$ в момент времени</strong></p><p>Подставляем значения времени $t=1$ с, $t=3$ с, $t=5$ с в уравнение движения:</p><p>При $t=1$ с: $x(1) = 5 \cdot 1 = 5$ м.</p><p>При $t=3$ с: $x(3) = 5 \cdot 3 = 15$ м.</p><p>При $t=5$ с: $x(5) = 5 \cdot 5 = 25$ м.</p><p><strong>Ответ:</strong> В моменты времени 1 с, 3 с, 5 с координата тела равна 5 м, 15 м, 25 м соответственно.</p><p><strong>Момент времени, когда координата $x$ тела равна...</strong></p><p>Решаем уравнение $x(t) = x_{final}$ относительно $t$ для каждого заданного значения координаты:</p><p>Для $x = 5$ м: $5 = 5t \implies t = \frac{5}{5} = 1$ с.</p><p>Для $x = 10$ м: $10 = 5t \implies t = \frac{10}{5} = 2$ с.</p><p>Для $x = 20$ м: $20 = 5t \implies t = \frac{20}{5} = 4$ с.</p><p><strong>Ответ:</strong> Координата равна 5 м в момент времени $t = 1$ с; 10 м в момент $t = 2$ с; 20 м в момент $t = 4$ с.</p><p><strong>Для закона движения $x(t) = -5 + 15t$</strong></p><p><strong>Начальная координата</strong></p><p>Свободный член в уравнении $x(t) = -5 + 15t$ равен -5.</p><p><strong>Ответ:</strong> $x_0 = -5$ м.</p><p><strong>Значение начальной скорости</strong></p><p>Коэффициент при $t$ в первой степени равен 15.</p><p><strong>Ответ:</strong> $v_0 = 15$ м/с.</p><p><strong>Значение начального ускорения</strong></p><p>Слагаемое с $t^2$ отсутствует, следовательно, ускорение $a=0$. Движение является равномерным прямолинейным.</p><p><strong>Ответ:</strong> $a = 0$ м/с².</p><p><strong>Координата $x$ в момент времени</strong></p><p>Подставляем значения времени $t=1$ с, $t=3$ с, $t=5$ с в уравнение движения:</p><p>При $t=1$ с: $x(1) = -5 + 15 \cdot 1 = 10$ м.</p><p>При $t=3$ с: $x(3) = -5 + 15 \cdot 3 = -5 + 45 = 40$ м.</p><p>При $t=5$ с: $x(5) = -5 + 15 \cdot 5 = -5 + 75 = 70$ м.</p><p><strong>Ответ:</strong> В моменты времени 1 с, 3 с, 5 с координата тела равна 10 м, 40 м, 70 м соответственно.</p><p><strong>Момент времени, когда координата $x$ тела равна...</strong></p><p>Для $x = 10$ м: $10 = -5 + 15t \implies 15t = 15 \implies t = 1$ с.</p><p>Для $x = 25$ м: $25 = -5 + 15t \implies 15t = 30 \implies t = 2$ с.</p><p>Для $x = 55$ м: $55 = -5 + 15t \implies 15t = 60 \implies t = 4$ с.</p><p><strong>Ответ:</strong> Координата равна 10 м в момент времени $t = 1$ с; 25 м в момент $t = 2$ с; 55 м в момент $t = 4$ с.</p><p><strong>Для закона движения $x(t) = 50 + 2t - 2.5t^2$</strong></p><p><strong>Начальная координата</strong></p><p>Свободный член в уравнении $x(t) = 50 + 2t - 2.5t^2$ равен 50.</p><p><strong>Ответ:</strong> $x_0 = 50$ м.</p><p><strong>Значение начальной скорости</strong></p><p>Коэффициент при $t$ в первой степени равен 2.</p><p><strong>Ответ:</strong> $v_0 = 2$ м/с.</p><p><strong>Значение начального ускорения</strong></p><p>Коэффициент при $t^2$ равен -2.5. Из общей формулы имеем $\frac{a}{2} = -2.5$, откуда $a = 2 \cdot (-2.5) = -5$. Движение является равноускоренным (равнозамедленным).</p><p><strong>Ответ:</strong> $a = -5$ м/с².</p><p><strong>Координата $x$ в момент времени</strong></p><p>Подставляем значения времени $t=1$ с, $t=3$ с, $t=5$ с в уравнение движения:</p><p>При $t=1$ с: $x(1) = 50 + 2 \cdot 1 - 2.5 \cdot 1^2 = 50 + 2 - 2.5 = 49.5$ м.</p><p>При $t=3$ с: $x(3) = 50 + 2 \cdot 3 - 2.5 \cdot 3^2 = 50 + 6 - 2.5 \cdot 9 = 56 - 22.5 = 33.5$ м.</p><p>При $t=5$ с: $x(5) = 50 + 2 \cdot 5 - 2.5 \cdot 5^2 = 50 + 10 - 2.5 \cdot 25 = 60 - 62.5 = -2.5$ м.</p><p><strong>Ответ:</strong> В моменты времени 1 с, 3 с, 5 с координата тела равна 49.5 м, 33.5 м, -2.5 м соответственно.</p><p><strong>Момент времени, когда координата $x$ тела равна...</strong></p><p>Для $x = 50$ м: $50 = 50 + 2t - 2.5t^2 \implies 0 = 2t - 2.5t^2 \implies t(2 - 2.5t) = 0$. Решениями являются $t_1 = 0$ с (начальный момент времени) и $2 - 2.5t = 0 \implies t_2 = \frac{2}{2.5} = 0.8$ с.</p><p>Для $x = 44$ м: $44 = 50 + 2t - 2.5t^2 \implies 2.5t^2 - 2t - 6 = 0$. Решаем квадратное уравнение. Дискриминант $D = (-2)^2 - 4 \cdot 2.5 \cdot (-6) = 4 + 60 = 64$. Корни уравнения: $t = \frac{2 \pm \sqrt{64}}{2 \cdot 2.5} = \frac{2 \pm 8}{5}$. Физический смысл имеет только положительный корень времени: $t = \frac{2+8}{5} = 2$ с.</p><p>Для $x = 18$ м: $18 = 50 + 2t - 2.5t^2 \implies 2.5t^2 - 2t - 32 = 0$. Решаем квадратное уравнение. Дискриминант $D = (-2)^2 - 4 \cdot 2.5 \cdot (-32) = 4 + 320 = 324$. Корни уравнения: $t = \frac{2 \pm \sqrt{324}}{2 \cdot 2.5} = \frac{2 \pm 18}{5}$. Физический смысл имеет только положительный корень времени: $t = \frac{2+18}{5} = 4$ с.</p><p><strong>Ответ:</strong> Координата равна 50 м в момент времени $t = 0.8$ с (помимо начального момента); 44 м в момент $t = 2$ с; 18 м в момент $t = 4$ с.</p>" ] #original: array:6 [ "id" => 1734264 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1261} "task" => array:2 [ "refs" => "1434890" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Законы движения трех тел:</p><p>1. $x(t) = 5t$</p><p>2. $x(t) = -5 + 15t$</p><p>3. $x(t) = 50 + 2t - 2.5t^2$</p><p>Координата $x$ измеряется в метрах (м), время $t$ – в секундах (с). Все величины представлены в системе СИ, перевод не требуется.</p><p><strong>Найти:</strong></p><p>Для каждого закона движения определить:</p><p>1. Начальную координату ($x_0$).</p><p>2. Значение начальной скорости ($v_0$).</p><p>3. Значение начального ускорения ($a$).</p><p>4. Координату $x$ в моменты времени $t=1$ с, $t=3$ с, $t=5$ с.</p><p>5. Момент времени $t$, когда координата $x$ тела принимает заданные значения.</p><p><strong>Решение:</strong></p><p>Общий вид закона равноускоренного прямолинейного движения вдоль оси X: $x(t) = x_0 + v_0 t + \frac{a t^2}{2}$.</p><p>Будем сравнивать каждый заданный закон движения с этой общей формулой и выполнять необходимые расчеты для заполнения таблицы.</p><p><strong>Для закона движения $x(t) = 5t$</strong></p><p><strong>Начальная координата</strong></p><p>Сравниваем уравнение $x(t) = 5t$ с общей формулой. Свободный член, соответствующий начальной координате $x_0$, отсутствует, следовательно, он равен нулю.</p><p><strong>Ответ:</strong> $x_0 = 0$ м.</p><p><strong>Значение начальной скорости</strong></p><p>Коэффициент при $t$ в первой степени соответствует начальной скорости $v_0$ и равен 5.</p><p><strong>Ответ:</strong> $v_0 = 5$ м/с.</p><p><strong>Значение начального ускорения</strong></p><p>Слагаемое с $t^2$ отсутствует, значит, коэффициент при нем $\frac{a}{2}$ равен нулю, следовательно, ускорение $a=0$. Движение является равномерным прямолинейным.</p><p><strong>Ответ:</strong> $a = 0$ м/с².</p><p><strong>Координата $x$ в момент времени</strong></p><p>Подставляем значения времени $t=1$ с, $t=3$ с, $t=5$ с в уравнение движения:</p><p>При $t=1$ с: $x(1) = 5 \cdot 1 = 5$ м.</p><p>При $t=3$ с: $x(3) = 5 \cdot 3 = 15$ м.</p><p>При $t=5$ с: $x(5) = 5 \cdot 5 = 25$ м.</p><p><strong>Ответ:</strong> В моменты времени 1 с, 3 с, 5 с координата тела равна 5 м, 15 м, 25 м соответственно.</p><p><strong>Момент времени, когда координата $x$ тела равна...</strong></p><p>Решаем уравнение $x(t) = x_{final}$ относительно $t$ для каждого заданного значения координаты:</p><p>Для $x = 5$ м: $5 = 5t \implies t = \frac{5}{5} = 1$ с.</p><p>Для $x = 10$ м: $10 = 5t \implies t = \frac{10}{5} = 2$ с.</p><p>Для $x = 20$ м: $20 = 5t \implies t = \frac{20}{5} = 4$ с.</p><p><strong>Ответ:</strong> Координата равна 5 м в момент времени $t = 1$ с; 10 м в момент $t = 2$ с; 20 м в момент $t = 4$ с.</p><p><strong>Для закона движения $x(t) = -5 + 15t$</strong></p><p><strong>Начальная координата</strong></p><p>Свободный член в уравнении $x(t) = -5 + 15t$ равен -5.</p><p><strong>Ответ:</strong> $x_0 = -5$ м.</p><p><strong>Значение начальной скорости</strong></p><p>Коэффициент при $t$ в первой степени равен 15.</p><p><strong>Ответ:</strong> $v_0 = 15$ м/с.</p><p><strong>Значение начального ускорения</strong></p><p>Слагаемое с $t^2$ отсутствует, следовательно, ускорение $a=0$. Движение является равномерным прямолинейным.</p><p><strong>Ответ:</strong> $a = 0$ м/с².</p><p><strong>Координата $x$ в момент времени</strong></p><p>Подставляем значения времени $t=1$ с, $t=3$ с, $t=5$ с в уравнение движения:</p><p>При $t=1$ с: $x(1) = -5 + 15 \cdot 1 = 10$ м.</p><p>При $t=3$ с: $x(3) = -5 + 15 \cdot 3 = -5 + 45 = 40$ м.</p><p>При $t=5$ с: $x(5) = -5 + 15 \cdot 5 = -5 + 75 = 70$ м.</p><p><strong>Ответ:</strong> В моменты времени 1 с, 3 с, 5 с координата тела равна 10 м, 40 м, 70 м соответственно.</p><p><strong>Момент времени, когда координата $x$ тела равна...</strong></p><p>Для $x = 10$ м: $10 = -5 + 15t \implies 15t = 15 \implies t = 1$ с.</p><p>Для $x = 25$ м: $25 = -5 + 15t \implies 15t = 30 \implies t = 2$ с.</p><p>Для $x = 55$ м: $55 = -5 + 15t \implies 15t = 60 \implies t = 4$ с.</p><p><strong>Ответ:</strong> Координата равна 10 м в момент времени $t = 1$ с; 25 м в момент $t = 2$ с; 55 м в момент $t = 4$ с.</p><p><strong>Для закона движения $x(t) = 50 + 2t - 2.5t^2$</strong></p><p><strong>Начальная координата</strong></p><p>Свободный член в уравнении $x(t) = 50 + 2t - 2.5t^2$ равен 50.</p><p><strong>Ответ:</strong> $x_0 = 50$ м.</p><p><strong>Значение начальной скорости</strong></p><p>Коэффициент при $t$ в первой степени равен 2.</p><p><strong>Ответ:</strong> $v_0 = 2$ м/с.</p><p><strong>Значение начального ускорения</strong></p><p>Коэффициент при $t^2$ равен -2.5. Из общей формулы имеем $\frac{a}{2} = -2.5$, откуда $a = 2 \cdot (-2.5) = -5$. Движение является равноускоренным (равнозамедленным).</p><p><strong>Ответ:</strong> $a = -5$ м/с².</p><p><strong>Координата $x$ в момент времени</strong></p><p>Подставляем значения времени $t=1$ с, $t=3$ с, $t=5$ с в уравнение движения:</p><p>При $t=1$ с: $x(1) = 50 + 2 \cdot 1 - 2.5 \cdot 1^2 = 50 + 2 - 2.5 = 49.5$ м.</p><p>При $t=3$ с: $x(3) = 50 + 2 \cdot 3 - 2.5 \cdot 3^2 = 50 + 6 - 2.5 \cdot 9 = 56 - 22.5 = 33.5$ м.</p><p>При $t=5$ с: $x(5) = 50 + 2 \cdot 5 - 2.5 \cdot 5^2 = 50 + 10 - 2.5 \cdot 25 = 60 - 62.5 = -2.5$ м.</p><p><strong>Ответ:</strong> В моменты времени 1 с, 3 с, 5 с координата тела равна 49.5 м, 33.5 м, -2.5 м соответственно.</p><p><strong>Момент времени, когда координата $x$ тела равна...</strong></p><p>Для $x = 50$ м: $50 = 50 + 2t - 2.5t^2 \implies 0 = 2t - 2.5t^2 \implies t(2 - 2.5t) = 0$. Решениями являются $t_1 = 0$ с (начальный момент времени) и $2 - 2.5t = 0 \implies t_2 = \frac{2}{2.5} = 0.8$ с.</p><p>Для $x = 44$ м: $44 = 50 + 2t - 2.5t^2 \implies 2.5t^2 - 2t - 6 = 0$. Решаем квадратное уравнение. Дискриминант $D = (-2)^2 - 4 \cdot 2.5 \cdot (-6) = 4 + 60 = 64$. Корни уравнения: $t = \frac{2 \pm \sqrt{64}}{2 \cdot 2.5} = \frac{2 \pm 8}{5}$. Физический смысл имеет только положительный корень времени: $t = \frac{2+8}{5} = 2$ с.</p><p>Для $x = 18$ м: $18 = 50 + 2t - 2.5t^2 \implies 2.5t^2 - 2t - 32 = 0$. Решаем квадратное уравнение. Дискриминант $D = (-2)^2 - 4 \cdot 2.5 \cdot (-32) = 4 + 320 = 324$. Корни уравнения: $t = \frac{2 \pm \sqrt{324}}{2 \cdot 2.5} = \frac{2 \pm 18}{5}$. Физический смысл имеет только положительный корень времени: $t = \frac{2+18}{5} = 4$ с.</p><p><strong>Ответ:</strong> Координата равна 50 м в момент времени $t = 0.8$ с (помимо начального момента); 44 м в момент $t = 2$ с; 18 м в момент $t = 4$ 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" => "1434891" "type" => "task" ] "previous" => array:2 [ "refs" => "1434889" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1286 #items: array:1 [ 0 => App\Models\Book {#1241 #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" => 1203 "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 {#1235 #items: array:1 [ 0 => App\Models\Term {#1236 #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" …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_class" => Illuminate\Database\Eloquent\Collection {#1243 #items: array:1 [ 0 => App\Models\Term {#1239 #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 {#1237 #items: array:1 [ 0 => App\Models\Term {#1240 #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 {#1238 #items: array:4 [ 0 => App\Models\Term {#1259 #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 {#1260 #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 {#1262 #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 {#1263 #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 {#1264 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1265 #items: array:1 [ 0 => App\Models\Term {#1266 #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 {#1267 #items: array:1 [ 0 => App\Models\Term {#1268 #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 {#1269 #items: array:1 [ 0 => App\Models\Term {#1270 #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 {#1271 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1272 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1273 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1274 #items: array:1 [ 0 => App\Models\Term {#1275 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ …10] #original: array:10 [ …10] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1276 #items: array:1 [ 0 => App\Models\Term {#1277 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1278 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "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" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ 0 => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" 1 => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" 2 => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" ] "field_cover_alts" => array:3 [ 0 => "" 1 => "" 2 => "" ] "field_covers" => array:3 [ 0 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" "alt" => "" "width" => "2293" "height" => "2989" ] 1 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" "alt" => "" "width" => "2265" "height" => "3003" ] 2 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" "alt" => "" "width" => "2241" "height" => "2999" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1279 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1280 #items: [] #escapeWhenCastingToString: false } "field_old_book" => 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№2 (с. 8)
Условие. №2 (с. 8)
скриншот условия
2. В таблице приведены законы движения тел вдоль оси $\text{X}$, в которых координату $\text{x}$ измеряют в метрах, а время $\text{t}$ – в секундах. Заполните таблицу.
Закон движения
Начальная координата
Значение
начальной скорости
начального ускорения
Координата $\text{x}$ в момент времени
1 с
3 с
5 с
Момент времени, когда координата $\text{x}$ тела равна
$x(t) = 5t$
5 м
Окончание
Закон движения
Начальная координата
Значение
начальной скорости
начального ускорения
Координата $\text{x}$ в момент времени
1 с
3 с
5 с
Момент времени, когда координата $\text{x}$ тела равна
$x(t) = 5t$
10 м
20 м
10 м
$x(t) = -5 + 15t$
25 м
55 м
50 м
$x(t) = 50 + 2t - 2,5t^2$
44 м
18 м
Решение. №2 (с. 8)
Дано:
Законы движения трех тел:
1. $x(t) = 5t$
2. $x(t) = -5 + 15t$
3. $x(t) = 50 + 2t - 2.5t^2$
Координата $x$ измеряется в метрах (м), время $t$ – в секундах (с). Все величины представлены в системе СИ, перевод не требуется.
Найти:
Для каждого закона движения определить:
1. Начальную координату ($x_0$).
2. Значение начальной скорости ($v_0$).
3. Значение начального ускорения ($a$).
4. Координату $x$ в моменты времени $t=1$ с, $t=3$ с, $t=5$ с.
5. Момент времени $t$, когда координата $x$ тела принимает заданные значения.
Решение:
Общий вид закона равноускоренного прямолинейного движения вдоль оси X: $x(t) = x_0 + v_0 t + \frac{a t^2}{2}$.
Будем сравнивать каждый заданный закон движения с этой общей формулой и выполнять необходимые расчеты для заполнения таблицы.
Для закона движения $x(t) = 5t$
Начальная координата
Сравниваем уравнение $x(t) = 5t$ с общей формулой. Свободный член, соответствующий начальной координате $x_0$, отсутствует, следовательно, он равен нулю.
Ответ: $x_0 = 0$ м.
Значение начальной скорости
Коэффициент при $t$ в первой степени соответствует начальной скорости $v_0$ и равен 5.
Ответ: $v_0 = 5$ м/с.
Значение начального ускорения
Слагаемое с $t^2$ отсутствует, значит, коэффициент при нем $\frac{a}{2}$ равен нулю, следовательно, ускорение $a=0$. Движение является равномерным прямолинейным.
Ответ: $a = 0$ м/с².
Координата $x$ в момент времени
Подставляем значения времени $t=1$ с, $t=3$ с, $t=5$ с в уравнение движения:
При $t=1$ с: $x(1) = 5 \cdot 1 = 5$ м.
При $t=3$ с: $x(3) = 5 \cdot 3 = 15$ м.
При $t=5$ с: $x(5) = 5 \cdot 5 = 25$ м.
Ответ: В моменты времени 1 с, 3 с, 5 с координата тела равна 5 м, 15 м, 25 м соответственно.
Момент времени, когда координата $x$ тела равна...
Решаем уравнение $x(t) = x_{final}$ относительно $t$ для каждого заданного значения координаты:
Для $x = 5$ м: $5 = 5t \implies t = \frac{5}{5} = 1$ с.
Для $x = 10$ м: $10 = 5t \implies t = \frac{10}{5} = 2$ с.
Для $x = 20$ м: $20 = 5t \implies t = \frac{20}{5} = 4$ с.
Ответ: Координата равна 5 м в момент времени $t = 1$ с; 10 м в момент $t = 2$ с; 20 м в момент $t = 4$ с.
Для закона движения $x(t) = -5 + 15t$
Начальная координата
Свободный член в уравнении $x(t) = -5 + 15t$ равен -5.
Ответ: $x_0 = -5$ м.
Значение начальной скорости
Коэффициент при $t$ в первой степени равен 15.
Ответ: $v_0 = 15$ м/с.
Значение начального ускорения
Слагаемое с $t^2$ отсутствует, следовательно, ускорение $a=0$. Движение является равномерным прямолинейным.
Ответ: $a = 0$ м/с².
Координата $x$ в момент времени
Подставляем значения времени $t=1$ с, $t=3$ с, $t=5$ с в уравнение движения:
При $t=1$ с: $x(1) = -5 + 15 \cdot 1 = 10$ м.
При $t=3$ с: $x(3) = -5 + 15 \cdot 3 = -5 + 45 = 40$ м.
При $t=5$ с: $x(5) = -5 + 15 \cdot 5 = -5 + 75 = 70$ м.
Ответ: В моменты времени 1 с, 3 с, 5 с координата тела равна 10 м, 40 м, 70 м соответственно.
Момент времени, когда координата $x$ тела равна...
Для $x = 10$ м: $10 = -5 + 15t \implies 15t = 15 \implies t = 1$ с.
Для $x = 25$ м: $25 = -5 + 15t \implies 15t = 30 \implies t = 2$ с.
Для $x = 55$ м: $55 = -5 + 15t \implies 15t = 60 \implies t = 4$ с.
Ответ: Координата равна 10 м в момент времени $t = 1$ с; 25 м в момент $t = 2$ с; 55 м в момент $t = 4$ с.
Для закона движения $x(t) = 50 + 2t - 2.5t^2$
Начальная координата
Свободный член в уравнении $x(t) = 50 + 2t - 2.5t^2$ равен 50.
Ответ: $x_0 = 50$ м.
Значение начальной скорости
Коэффициент при $t$ в первой степени равен 2.
Ответ: $v_0 = 2$ м/с.
Значение начального ускорения
Коэффициент при $t^2$ равен -2.5. Из общей формулы имеем $\frac{a}{2} = -2.5$, откуда $a = 2 \cdot (-2.5) = -5$. Движение является равноускоренным (равнозамедленным).
Ответ: $a = -5$ м/с².
Координата $x$ в момент времени
Подставляем значения времени $t=1$ с, $t=3$ с, $t=5$ с в уравнение движения:
При $t=1$ с: $x(1) = 50 + 2 \cdot 1 - 2.5 \cdot 1^2 = 50 + 2 - 2.5 = 49.5$ м.
При $t=3$ с: $x(3) = 50 + 2 \cdot 3 - 2.5 \cdot 3^2 = 50 + 6 - 2.5 \cdot 9 = 56 - 22.5 = 33.5$ м.
При $t=5$ с: $x(5) = 50 + 2 \cdot 5 - 2.5 \cdot 5^2 = 50 + 10 - 2.5 \cdot 25 = 60 - 62.5 = -2.5$ м.
Ответ: В моменты времени 1 с, 3 с, 5 с координата тела равна 49.5 м, 33.5 м, -2.5 м соответственно.
Момент времени, когда координата $x$ тела равна...
Для $x = 50$ м: $50 = 50 + 2t - 2.5t^2 \implies 0 = 2t - 2.5t^2 \implies t(2 - 2.5t) = 0$. Решениями являются $t_1 = 0$ с (начальный момент времени) и $2 - 2.5t = 0 \implies t_2 = \frac{2}{2.5} = 0.8$ с.
Для $x = 44$ м: $44 = 50 + 2t - 2.5t^2 \implies 2.5t^2 - 2t - 6 = 0$. Решаем квадратное уравнение. Дискриминант $D = (-2)^2 - 4 \cdot 2.5 \cdot (-6) = 4 + 60 = 64$. Корни уравнения: $t = \frac{2 \pm \sqrt{64}}{2 \cdot 2.5} = \frac{2 \pm 8}{5}$. Физический смысл имеет только положительный корень времени: $t = \frac{2+8}{5} = 2$ с.
Для $x = 18$ м: $18 = 50 + 2t - 2.5t^2 \implies 2.5t^2 - 2t - 32 = 0$. Решаем квадратное уравнение. Дискриминант $D = (-2)^2 - 4 \cdot 2.5 \cdot (-32) = 4 + 320 = 324$. Корни уравнения: $t = \frac{2 \pm \sqrt{324}}{2 \cdot 2.5} = \frac{2 \pm 18}{5}$. Физический смысл имеет только положительный корень времени: $t = \frac{2+18}{5} = 4$ с.
Ответ: Координата равна 50 м в момент времени $t = 0.8$ с (помимо начального момента); 44 м в момент $t = 2$ с; 18 м в момент $t = 4$ с.
Другие задания:
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