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Номер 40, страница 16, 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 1. Система отсчёта, траектория, путь и перемещение - номер 40, страница 16.
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" => 1433310 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "16" "field_page_end" => "17" "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/01-40" "field_display_title" => "40" "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 {#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 {#1183 #items: array:4 [ 0 => App\Models\Branch {#1193 #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 {#1197 #items: array:1 [ 0 => App\Models\Term {#1194 #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 {#1229 #items: array:1 [ 0 => App\Models\Book {#1196 #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 {#1198 #items: array:1 [ 0 => App\Models\Term {#1195 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ …6] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #original: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ …6] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1199 #items: array:1 [ 0 => App\Models\Term {#1200 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ …6] "field_translit" => "devjatyj" ] #original: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ …6] "field_translit" => "devjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1201 #items: array:1 [ 0 => App\Models\Term {#1202 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5208 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Бином" "field_cases" => null "field_translit" => "binom" ] #original: array:6 [ "id" => 5208 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Бином" "field_cases" => null "field_translit" => "binom" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1203 #items: array:4 [ 0 => App\Models\Term {#1204 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4104 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Генденштейн" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Лев" "field_patronymic" => "Элевич" "field_surname_rp" => "Генденштейна" ] #original: array:12 [ "id" => 4104 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Генденштейн" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Лев" "field_patronymic" => "Элевич" "field_surname_rp" => "Генденштейна" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1205 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 3936 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Булатова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Альбина" "field_patronymic" => "Александрова" "field_surname_rp" => null ] #original: array:12 [ "id" => 3936 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Булатова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Альбина" "field_patronymic" => "Александрова" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Term {#1206 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4679 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Корнильев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Игорь" "field_patronymic" => "Николаевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4679 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Корнильев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Игорь" "field_patronymic" => "Николаевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Term {#1207 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4758 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кошкина" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Анжелика" "field_patronymic" => "Васильевна" "field_surname_rp" => null ] #original: array:12 [ "id" => 4758 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кошкина" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Анжелика" "field_patronymic" => "Васильевна" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1208 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1209 #items: array:1 [ 0 => App\Models\Term {#1210 #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" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #original: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1211 #items: array:1 [ 0 => App\Models\Term {#1212 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ …6] "field_translit" => "rossiya" ] #original: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ …6] "field_translit" => "rossiya" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1213 #items: array:1 [ 0 => App\Models\Term {#1214 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ …6] "field_translit" => "moskva" ] #original: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ …6] "field_translit" => "moskva" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1215 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1216 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1217 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1218 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1219 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1220 #items: array:1 [ 0 => App\Models\Term {#1221 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 5395 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Орлов" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Алексеевич" "field_surname_rp" => "Орлова" ] #original: array:12 [ "id" => 5395 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Орлов" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Алексеевич" "field_surname_rp" => "Орлова" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_under_the_edition_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 {#1222 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1223 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1224 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1225 #items: array:1 [ 0 => App\Models\Term {#1226 #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" => 6978 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "бирюзовый" "field_cases" => array:6 [ …6] "field_translit" => "biruzovyy" ] #original: array:6 [ "id" => 6978 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "бирюзовый" "field_cases" => array:6 [ …6] "field_translit" => "biruzovyy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 556 "class_subject" => 493 ] ] #original: array:50 [ "id" => 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 {#1198} "field_class" => Illuminate\Database\Eloquent\Collection {#1199} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1201} "field_author" => Illuminate\Database\Eloquent\Collection {#1203} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1208} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1209} "field_country" => Illuminate\Database\Eloquent\Collection {#1211} "field_city" => Illuminate\Database\Eloquent\Collection {#1213} "field_series" => Illuminate\Database\Eloquent\Collection {#1215} "field_umk" => Illuminate\Database\Eloquent\Collection {#1216} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1217} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1218} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1219} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1220} "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 {#1222} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1223} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1224} "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1225} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 556 "class_subject" => 493 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1227 #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 {#1197} "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 {#1229} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1227} ] #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 {#1228 #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 {#1230 #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 {#1231 #items: array:1 [ 0 => App\Models\Book {#1196} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1232 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #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 {#1230} "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 {#1231} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1232} ] #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 {#1233 #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 {#1237 #items: array:1 [ 0 => App\Models\Term {#1234 #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 {#1236 #items: array:1 [ 0 => App\Models\Book {#1196} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1310 #items: array:1 [ 0 => App\Models\Branch {#1235 #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 {#1239 …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 {#1238 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1271 …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 {#1239 …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 {#1238 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1271 …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 {#1237} "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 {#1236} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1310} ] #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 {#1308 #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" => 1433209 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Система отсчёта, траектория, путь и перемещение" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1313 #items: array:1 [ 0 => App\Models\Term {#1309 #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" => "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 {#1312 #items: array:1 [ 0 => App\Models\Book {#1196} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1321 #items: array:1 [ 0 => App\Models\Branch {#1320 #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 {#1322 …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 {#1323 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1324 …2} ] #original: array:24 [ "id" => 1433208 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Кинематика" "field_branch_order" => "I" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1322 …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 {#1323 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1324 …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" => 1433209 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Система отсчёта, траектория, путь и перемещение" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1313} "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 {#1312} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1321} ] #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 {#1110 #items: array:2 [ 0 => App\Models\Element {#1176 #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" => 1696051 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1166 #items: array:1 [ 0 => App\Models\Edition {#1175 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 6168 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1174 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1172 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1171 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1170 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6168 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1174 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1172 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1171 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1170 …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" => "1433310" "type" => "task" ] "text" => "<p><strong>40.</strong> Изобразите в тетради траекторию материальной точки, при движении по которой пройденный путь больше, чем модуль перемещения:</p><p><strong>а)</strong> в 3 раза;</p><p><strong>б)</strong> в $\frac{\pi}{2}$ раз;</p><p><strong>в)</strong> в $\sqrt{2}$ раз.</p>" "img" => array:2 [ 0 => array:5 [ "name" => "40-1.jpg" "alt" => null "width" => "1597" "height" => 251 "path" => "/media/fizika_09/gendenshtejn-u/0-01/40-1.webp?ts=1759348123" ] 1 => array:5 [ "name" => "40-2.jpg" "alt" => null "width" => "812" "height" => 330 "path" => "/media/fizika_09/gendenshtejn-u/0-01/40-2.webp?ts=1759348123" ] ] ] #original: array:7 [ "id" => 1696051 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1166} "task" => array:2 [ "refs" => "1433310" "type" => "task" ] "text" => "<p><strong>40.</strong> Изобразите в тетради траекторию материальной точки, при движении по которой пройденный путь больше, чем модуль перемещения:</p><p><strong>а)</strong> в 3 раза;</p><p><strong>б)</strong> в $\frac{\pi}{2}$ раз;</p><p><strong>в)</strong> в $\sqrt{2}$ раз.</p>" "img" => array:2 [ 0 => array:5 [ "name" => "40-1.jpg" "alt" => null "width" => "1597" "height" => 251 "path" => "/media/fizika_09/gendenshtejn-u/0-01/40-1.webp?ts=1759348123" ] 1 => array:5 [ "name" => "40-2.jpg" "alt" => null "width" => "812" "height" => 330 "path" => "/media/fizika_09/gendenshtejn-u/0-01/40-2.webp?ts=1759348123" ] ] ] #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 {#1169 #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" => 1780121 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1160 #items: array:1 [ 0 => App\Models\Edition {#1168 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 6515 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1164 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1165 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1162 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1163 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6515 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1164 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1165 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1162 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1163 …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" => "1433310" "type" => "task" ] "text" => "<p>Для решения задачи необходимо найти такую траекторию движения, для которой отношение длины траектории (пройденного пути $\text{S}$) к длине отрезка, соединяющего начальную и конечную точки (модулю перемещения $|\Delta\vec{r}|$), будет равно заданному числу.</p><p><strong>а) в 3 раза</strong></p><p><strong>Дано:</strong></p><p>Отношение пройденного пути $\text{S}$ к модулю перемещения $|\Delta\vec{r}|$ равно 3.</p><p>$ \frac{S}{|\Delta\vec{r}|} = 3 $</p><p><strong>Найти:</strong></p><p>Изобразить и описать траекторию движения.</p><p><strong>Решение:</strong></p><p>Рассмотрим самый простой случай криволинейного движения – движение по прямой с возвратом. Пусть материальная точка движется по прямой из начальной точки А в точку В, пройдя расстояние $\text{L}$. Затем точка разворачивается и движется в обратном направлении до точки С на расстояние $\text{d}$.</p><p>В этом случае пройденный путь $\text{S}$ будет равен сумме длин отрезков АВ и ВС:</p><p>$ S = L + d $</p><p>Перемещение – это вектор, соединяющий начальную и конечную точки, то есть вектор $\vec{AC}$. Модуль перемещения $|\Delta\vec{r}|$ равен длине отрезка АС:</p><p>$ |\Delta\vec{r}| = L - d $</p><p>Согласно условию задачи, отношение пути к модулю перемещения равно 3:</p><p>$ \frac{S}{|\Delta\vec{r}|} = \frac{L+d}{L-d} = 3 $</p><p>Решим это уравнение относительно $\text{d}$:</p><p>$ L + d = 3(L - d) $</p><p>$ L + d = 3L - 3d $</p><p>$ 4d = 2L $</p><p>$ d = \frac{L}{2} $</p><p>Таким образом, точка должна пройти расстояние $\text{L}$ в одном направлении, а затем вернуться на половину этого расстояния ($L/2$) назад.</p><p><strong>Ответ:</strong> Траекторией является движение по прямой на некоторое расстояние $\text{L}$ из точки А в точку В, а затем движение в обратном направлении на расстояние $L/2$ до точки С, которая является серединой отрезка АВ.<br><svg width="220" height="60" xmlns="http://www.w3.org/2000/svg"><defs><marker id="arrow_a" markerWidth="10" markerHeight="7" refX="10" refY="3.5" orient="auto"><polygon points="0 0, 10 3.5, 0 7"></polygon></marker><marker id="arrow_a_rev" markerWidth="10" markerHeight="7" refX="0" refY="3.5" orient="auto-start-reverse"><polygon points="0 0, 10 3.5, 0 7" fill="red"></polygon></marker></defs><line x1="10" y1="20" x2="210" y2="20" stroke="black" stroke-width="2" marker-end="url(#arrow_a)"></line><line x1="210" y1="30" x2="110" y2="30" stroke="red" stroke-width="2" marker-end="url(#arrow_a_rev)"></line><circle cx="10" cy="20" r="3" fill="blue"></circle><text x="5" y="50" font-size="12">A (старт)</text><circle cx="210" cy="20" r="3" fill="green"></circle><text x="208" y="10" font-size="12">B</text><circle cx="110" cy="30" r="3" fill="red"></circle><text x="95" y="50" font-size="12">C (финиш)</text></svg></p><p><strong>б) в $\frac{\pi}{2}$ раз</strong></p><p><strong>Дано:</strong></p><p>Отношение пройденного пути $\text{S}$ к модулю перемещения $|\Delta\vec{r}|$ равно $\frac{\pi}{2}$.</p><p>$ \frac{S}{|\Delta\vec{r}|} = \frac{\pi}{2} $</p><p><strong>Найти:</strong></p><p>Изобразить и описать траекторию движения.</p><p><strong>Решение:</strong></p><p>Рассмотрим движение материальной точки по дуге окружности. Пусть точка движется по полуокружности радиуса $\text{R}$ из начальной точки А в конечную точку В.</p><p>Пройденный путь $\text{S}$ равен длине полуокружности:</p><p>$ S = \pi R $</p><p>Перемещение – это вектор, соединяющий начальную и конечную точки, то есть вектор $\vec{AB}$. Модуль перемещения $|\Delta\vec{r}|$ равен длине диаметра окружности, соединяющего точки А и В:</p><p>$ |\Delta\vec{r}| = 2R $</p><p>Найдем отношение пути к модулю перемещения:</p><p>$ \frac{S}{|\Delta\vec{r}|} = \frac{\pi R}{2R} = \frac{\pi}{2} $</p><p>Это в точности соответствует условию задачи.</p><p><strong>Ответ:</strong> Траекторией является полуокружность. Точка начинает движение в одном конце диаметра и заканчивает в другом.<br><svg width="220" height="120" xmlns="http://www.w3.org/2000/svg"><defs><marker id="arrow_b" markerWidth="10" markerHeight="7" refX="0" refY="3.5" orient="auto"><polygon points="0 0, 10 3.5, 0 7"></polygon></marker></defs><path d="M 10 100 A 100 100 0 0 1 210 100" stroke="black" stroke-width="2" fill="none" marker-end="url(#arrow_b)"></path><line x1="10" y1="100" x2="210" y2="100" stroke="red" stroke-dasharray="4" stroke-width="2"></line><circle cx="10" cy="100" r="3" fill="blue"></circle><text x="5" y="115" font-size="12">A (старт)</text><circle cx="210" cy="100" r="3" fill="red"></circle><text x="180" y="115" font-size="12">B (финиш)</text></svg></p><p><strong>в) в $\sqrt{2}$ раз</strong></p><p><strong>Дано:</strong></p><p>Отношение пройденного пути $\text{S}$ к модулю перемещения $|\Delta\vec{r}|$ равно $\sqrt{2}$.</p><p>$ \frac{S}{|\Delta\vec{r}|} = \sqrt{2} $</p><p><strong>Найти:</strong></p><p>Изобразить и описать траекторию движения.</p><p><strong>Решение:</strong></p><p>Рассмотрим движение точки по траектории, состоящей из двух одинаковых прямолинейных отрезков, расположенных под прямым углом друг к другу. Пусть точка движется из А в В, а затем из В в С, причем $AB = BC = L$ и угол $\angle ABC = 90^\circ$.</p><p>Пройденный путь $\text{S}$ равен сумме длин отрезков АВ и ВС:</p><p>$ S = AB + BC = L + L = 2L $</p><p>Перемещение – это вектор $\vec{AC}$. Его модуль $|\Delta\vec{r}|$ равен длине гипотенузы прямоугольного треугольника АВС. По теореме Пифагора:</p><p>$ |\Delta\vec{r}| = AC = \sqrt{AB^2 + BC^2} = \sqrt{L^2 + L^2} = \sqrt{2L^2} = L\sqrt{2} $</p><p>Найдем отношение пути к модулю перемещения:</p><p>$ \frac{S}{|\Delta\vec{r}|} = \frac{2L}{L\sqrt{2}} = \frac{2}{\sqrt{2}} = \sqrt{2} $</p><p>Это в точности соответствует условию задачи.</p><p><strong>Ответ:</strong> Траекторией является ломаная линия, состоящая из двух равных отрезков, расположенных под прямым углом друг к другу.<br><svg width="150" height="150" xmlns="http://www.w3.org/2000/svg"><defs><marker id="arrow_c" markerWidth="10" markerHeight="7" refX="0" refY="3.5" orient="auto"><polygon points="0 0, 10 3.5, 0 7"></polygon></marker></defs><line x1="20" y1="20" x2="20" y2="120" stroke="black" stroke-width="2" marker-end="url(#arrow_c)"></line><line x1="20" y1="120" x2="120" y2="120" stroke="black" stroke-width="2" marker-end="url(#arrow_c)"></line><line x1="20" y1="20" x2="120" y2="120" stroke="red" stroke-dasharray="4" stroke-width="2"></line><circle cx="20" cy="20" r="3" fill="blue"></circle><text x="25" y="25" font-size="12">A (старт)</text><circle cx="20" cy="120" r="3" fill="green"></circle><text x="25" y="125" font-size="12">B</text><circle cx="120" cy="120" r="3" fill="red"></circle><text x="95" y="135" font-size="12">C (финиш)</text></svg></p>" ] #original: array:6 [ "id" => 1780121 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1160} "task" => array:2 [ "refs" => "1433310" "type" => "task" ] "text" => "<p>Для решения задачи необходимо найти такую траекторию движения, для которой отношение длины траектории (пройденного пути $\text{S}$) к длине отрезка, соединяющего начальную и конечную точки (модулю перемещения $|\Delta\vec{r}|$), будет равно заданному числу.</p><p><strong>а) в 3 раза</strong></p><p><strong>Дано:</strong></p><p>Отношение пройденного пути $\text{S}$ к модулю перемещения $|\Delta\vec{r}|$ равно 3.</p><p>$ \frac{S}{|\Delta\vec{r}|} = 3 $</p><p><strong>Найти:</strong></p><p>Изобразить и описать траекторию движения.</p><p><strong>Решение:</strong></p><p>Рассмотрим самый простой случай криволинейного движения – движение по прямой с возвратом. Пусть материальная точка движется по прямой из начальной точки А в точку В, пройдя расстояние $\text{L}$. Затем точка разворачивается и движется в обратном направлении до точки С на расстояние $\text{d}$.</p><p>В этом случае пройденный путь $\text{S}$ будет равен сумме длин отрезков АВ и ВС:</p><p>$ S = L + d $</p><p>Перемещение – это вектор, соединяющий начальную и конечную точки, то есть вектор $\vec{AC}$. Модуль перемещения $|\Delta\vec{r}|$ равен длине отрезка АС:</p><p>$ |\Delta\vec{r}| = L - d $</p><p>Согласно условию задачи, отношение пути к модулю перемещения равно 3:</p><p>$ \frac{S}{|\Delta\vec{r}|} = \frac{L+d}{L-d} = 3 $</p><p>Решим это уравнение относительно $\text{d}$:</p><p>$ L + d = 3(L - d) $</p><p>$ L + d = 3L - 3d $</p><p>$ 4d = 2L $</p><p>$ d = \frac{L}{2} $</p><p>Таким образом, точка должна пройти расстояние $\text{L}$ в одном направлении, а затем вернуться на половину этого расстояния ($L/2$) назад.</p><p><strong>Ответ:</strong> Траекторией является движение по прямой на некоторое расстояние $\text{L}$ из точки А в точку В, а затем движение в обратном направлении на расстояние $L/2$ до точки С, которая является серединой отрезка АВ.<br><svg width="220" height="60" xmlns="http://www.w3.org/2000/svg"><defs><marker id="arrow_a" markerWidth="10" markerHeight="7" refX="10" refY="3.5" orient="auto"><polygon points="0 0, 10 3.5, 0 7"></polygon></marker><marker id="arrow_a_rev" markerWidth="10" markerHeight="7" refX="0" refY="3.5" orient="auto-start-reverse"><polygon points="0 0, 10 3.5, 0 7" fill="red"></polygon></marker></defs><line x1="10" y1="20" x2="210" y2="20" stroke="black" stroke-width="2" marker-end="url(#arrow_a)"></line><line x1="210" y1="30" x2="110" y2="30" stroke="red" stroke-width="2" marker-end="url(#arrow_a_rev)"></line><circle cx="10" cy="20" r="3" fill="blue"></circle><text x="5" y="50" font-size="12">A (старт)</text><circle cx="210" cy="20" r="3" fill="green"></circle><text x="208" y="10" font-size="12">B</text><circle cx="110" cy="30" r="3" fill="red"></circle><text x="95" y="50" font-size="12">C (финиш)</text></svg></p><p><strong>б) в $\frac{\pi}{2}$ раз</strong></p><p><strong>Дано:</strong></p><p>Отношение пройденного пути $\text{S}$ к модулю перемещения $|\Delta\vec{r}|$ равно $\frac{\pi}{2}$.</p><p>$ \frac{S}{|\Delta\vec{r}|} = \frac{\pi}{2} $</p><p><strong>Найти:</strong></p><p>Изобразить и описать траекторию движения.</p><p><strong>Решение:</strong></p><p>Рассмотрим движение материальной точки по дуге окружности. Пусть точка движется по полуокружности радиуса $\text{R}$ из начальной точки А в конечную точку В.</p><p>Пройденный путь $\text{S}$ равен длине полуокружности:</p><p>$ S = \pi R $</p><p>Перемещение – это вектор, соединяющий начальную и конечную точки, то есть вектор $\vec{AB}$. Модуль перемещения $|\Delta\vec{r}|$ равен длине диаметра окружности, соединяющего точки А и В:</p><p>$ |\Delta\vec{r}| = 2R $</p><p>Найдем отношение пути к модулю перемещения:</p><p>$ \frac{S}{|\Delta\vec{r}|} = \frac{\pi R}{2R} = \frac{\pi}{2} $</p><p>Это в точности соответствует условию задачи.</p><p><strong>Ответ:</strong> Траекторией является полуокружность. Точка начинает движение в одном конце диаметра и заканчивает в другом.<br><svg width="220" height="120" xmlns="http://www.w3.org/2000/svg"><defs><marker id="arrow_b" markerWidth="10" markerHeight="7" refX="0" refY="3.5" orient="auto"><polygon points="0 0, 10 3.5, 0 7"></polygon></marker></defs><path d="M 10 100 A 100 100 0 0 1 210 100" stroke="black" stroke-width="2" fill="none" marker-end="url(#arrow_b)"></path><line x1="10" y1="100" x2="210" y2="100" stroke="red" stroke-dasharray="4" stroke-width="2"></line><circle cx="10" cy="100" r="3" fill="blue"></circle><text x="5" y="115" font-size="12">A (старт)</text><circle cx="210" cy="100" r="3" fill="red"></circle><text x="180" y="115" font-size="12">B (финиш)</text></svg></p><p><strong>в) в $\sqrt{2}$ раз</strong></p><p><strong>Дано:</strong></p><p>Отношение пройденного пути $\text{S}$ к модулю перемещения $|\Delta\vec{r}|$ равно $\sqrt{2}$.</p><p>$ \frac{S}{|\Delta\vec{r}|} = \sqrt{2} $</p><p><strong>Найти:</strong></p><p>Изобразить и описать траекторию движения.</p><p><strong>Решение:</strong></p><p>Рассмотрим движение точки по траектории, состоящей из двух одинаковых прямолинейных отрезков, расположенных под прямым углом друг к другу. Пусть точка движется из А в В, а затем из В в С, причем $AB = BC = L$ и угол $\angle ABC = 90^\circ$.</p><p>Пройденный путь $\text{S}$ равен сумме длин отрезков АВ и ВС:</p><p>$ S = AB + BC = L + L = 2L $</p><p>Перемещение – это вектор $\vec{AC}$. Его модуль $|\Delta\vec{r}|$ равен длине гипотенузы прямоугольного треугольника АВС. По теореме Пифагора:</p><p>$ |\Delta\vec{r}| = AC = \sqrt{AB^2 + BC^2} = \sqrt{L^2 + L^2} = \sqrt{2L^2} = L\sqrt{2} $</p><p>Найдем отношение пути к модулю перемещения:</p><p>$ \frac{S}{|\Delta\vec{r}|} = \frac{2L}{L\sqrt{2}} = \frac{2}{\sqrt{2}} = \sqrt{2} $</p><p>Это в точности соответствует условию задачи.</p><p><strong>Ответ:</strong> Траекторией является ломаная линия, состоящая из двух равных отрезков, расположенных под прямым углом друг к другу.<br><svg width="150" height="150" xmlns="http://www.w3.org/2000/svg"><defs><marker id="arrow_c" markerWidth="10" markerHeight="7" refX="0" refY="3.5" orient="auto"><polygon points="0 0, 10 3.5, 0 7"></polygon></marker></defs><line x1="20" y1="20" x2="20" y2="120" stroke="black" stroke-width="2" marker-end="url(#arrow_c)"></line><line x1="20" y1="120" x2="120" y2="120" stroke="black" stroke-width="2" marker-end="url(#arrow_c)"></line><line x1="20" y1="20" x2="120" y2="120" stroke="red" stroke-dasharray="4" stroke-width="2"></line><circle cx="20" cy="20" r="3" fill="blue"></circle><text x="25" y="25" font-size="12">A (старт)</text><circle cx="20" cy="120" r="3" fill="green"></circle><text x="25" y="125" font-size="12">B</text><circle cx="120" cy="120" r="3" fill="red"></circle><text x="95" y="135" font-size="12">C (финиш)</text></svg></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" => "1433311" "type" => "task" ] "previous" => array:2 [ "refs" => "1433309" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1178 #items: array:1 [ 0 => App\Models\Book {#1196} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1180 #items: array:1 [ 0 => App\Models\BookPage {#1149 #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" => 1434657 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "16" "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/page-2-16" "field_display_title" => "16" "field_folder" => "2" "field_image_name" => "16" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1121 #items: array:1 [ 0 => App\Models\Branch {#1161 #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" => 1433262 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1159 …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 {#1158 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1124 …2} ] #original: array:24 [ "id" => 1433262 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1159 …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 {#1158 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1124 …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 } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1123 #items: array:1 [ 0 => App\Models\Book {#1196} ] #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 {#1122 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1077 #items: array:1 [ 0 => App\Models\Element {#1109 #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" => 1697380 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1078 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1697380 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1078 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #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" => "1434658" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1434656" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1118 #items: array:3 [ 0 => App\Models\Task {#1104 #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" => 1433976 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "16" "field_page_end" => null "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/25-1" "field_display_title" => "1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1102 …2} "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 {#1103 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1101 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1550 …2} "content" => Illuminate\Database\Eloquent\Collection {#1551 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1558 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1433976 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "16" "field_page_end" => null "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/25-1" "field_display_title" => "1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1102 …2} "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 {#1103 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1101 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1550 …2} "content" => Illuminate\Database\Eloquent\Collection {#1551 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1558 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Task {#1553 #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" => 1433977 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "16" "field_page_end" => null "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/25-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1552 …2} "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 {#1560 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1556 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1554 …2} "content" => Illuminate\Database\Eloquent\Collection {#1555 …2} "next" => array:2 [ …2] …3 ] #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 {#1565 #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" => 1434657 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "16" "field_url" => "/9-klass/fizika/gendenshtejn-uchebnik/page-2-16" "field_display_title" => "16" "field_folder" => "2" "field_image_name" => "16" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1121} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1123} "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 {#1122} "content" => Illuminate\Database\Eloquent\Collection {#1077} "next" => array:2 [ "refs" => "1434658" "type" => "book_page" ] 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№40 (с. 16)
Условие. №40 (с. 16)
скриншот условия
40. Изобразите в тетради траекторию материальной точки, при движении по которой пройденный путь больше, чем модуль перемещения:
а) в 3 раза;
б) в $\frac{\pi}{2}$ раз;
в) в $\sqrt{2}$ раз.
Решение. №40 (с. 16)
Для решения задачи необходимо найти такую траекторию движения, для которой отношение длины траектории (пройденного пути $\text{S}$) к длине отрезка, соединяющего начальную и конечную точки (модулю перемещения $|\Delta\vec{r}|$), будет равно заданному числу.
а) в 3 раза
Дано:
Отношение пройденного пути $\text{S}$ к модулю перемещения $|\Delta\vec{r}|$ равно 3.
$ \frac{S}{|\Delta\vec{r}|} = 3 $
Найти:
Изобразить и описать траекторию движения.
Решение:
Рассмотрим самый простой случай криволинейного движения – движение по прямой с возвратом. Пусть материальная точка движется по прямой из начальной точки А в точку В, пройдя расстояние $\text{L}$. Затем точка разворачивается и движется в обратном направлении до точки С на расстояние $\text{d}$.
В этом случае пройденный путь $\text{S}$ будет равен сумме длин отрезков АВ и ВС:
$ S = L + d $
Перемещение – это вектор, соединяющий начальную и конечную точки, то есть вектор $\vec{AC}$. Модуль перемещения $|\Delta\vec{r}|$ равен длине отрезка АС:
$ |\Delta\vec{r}| = L - d $
Согласно условию задачи, отношение пути к модулю перемещения равно 3:
$ \frac{S}{|\Delta\vec{r}|} = \frac{L+d}{L-d} = 3 $
Решим это уравнение относительно $\text{d}$:
$ L + d = 3(L - d) $
$ L + d = 3L - 3d $
$ 4d = 2L $
$ d = \frac{L}{2} $
Таким образом, точка должна пройти расстояние $\text{L}$ в одном направлении, а затем вернуться на половину этого расстояния ($L/2$) назад.
Ответ: Траекторией является движение по прямой на некоторое расстояние $\text{L}$ из точки А в точку В, а затем движение в обратном направлении на расстояние $L/2$ до точки С, которая является серединой отрезка АВ.
б) в $\frac{\pi}{2}$ раз
Дано:
Отношение пройденного пути $\text{S}$ к модулю перемещения $|\Delta\vec{r}|$ равно $\frac{\pi}{2}$.
$ \frac{S}{|\Delta\vec{r}|} = \frac{\pi}{2} $
Найти:
Изобразить и описать траекторию движения.
Решение:
Рассмотрим движение материальной точки по дуге окружности. Пусть точка движется по полуокружности радиуса $\text{R}$ из начальной точки А в конечную точку В.
Пройденный путь $\text{S}$ равен длине полуокружности:
$ S = \pi R $
Перемещение – это вектор, соединяющий начальную и конечную точки, то есть вектор $\vec{AB}$. Модуль перемещения $|\Delta\vec{r}|$ равен длине диаметра окружности, соединяющего точки А и В:
$ |\Delta\vec{r}| = 2R $
Найдем отношение пути к модулю перемещения:
$ \frac{S}{|\Delta\vec{r}|} = \frac{\pi R}{2R} = \frac{\pi}{2} $
Это в точности соответствует условию задачи.
Ответ: Траекторией является полуокружность. Точка начинает движение в одном конце диаметра и заканчивает в другом.
в) в $\sqrt{2}$ раз
Дано:
Отношение пройденного пути $\text{S}$ к модулю перемещения $|\Delta\vec{r}|$ равно $\sqrt{2}$.
$ \frac{S}{|\Delta\vec{r}|} = \sqrt{2} $
Найти:
Изобразить и описать траекторию движения.
Решение:
Рассмотрим движение точки по траектории, состоящей из двух одинаковых прямолинейных отрезков, расположенных под прямым углом друг к другу. Пусть точка движется из А в В, а затем из В в С, причем $AB = BC = L$ и угол $\angle ABC = 90^\circ$.
Пройденный путь $\text{S}$ равен сумме длин отрезков АВ и ВС:
$ S = AB + BC = L + L = 2L $
Перемещение – это вектор $\vec{AC}$. Его модуль $|\Delta\vec{r}|$ равен длине гипотенузы прямоугольного треугольника АВС. По теореме Пифагора:
$ |\Delta\vec{r}| = AC = \sqrt{AB^2 + BC^2} = \sqrt{L^2 + L^2} = \sqrt{2L^2} = L\sqrt{2} $
Найдем отношение пути к модулю перемещения:
$ \frac{S}{|\Delta\vec{r}|} = \frac{2L}{L\sqrt{2}} = \frac{2}{\sqrt{2}} = \sqrt{2} $
Это в точности соответствует условию задачи.
Ответ: Траекторией является ломаная линия, состоящая из двух равных отрезков, расположенных под прямым углом друг к другу.
Другие задания:
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