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Номер 1.5, страница 4 - гдз по физике 9 класс задачник Артеменков, Ломаченков
Авторы: Артеменков Д. А., Ломаченков И. А., Панебратцев Ю. А.
Тип: Задачник
Серия: сферы
Издательство: Просвещение
Год издания: 2011 - 2026
Цвет обложки: синий
ISBN: 978-5-09-038216-8
Популярные ГДЗ в 9 классе
I. Движение тел вблизи поверхности Земли и гравитация - номер 1.5, страница 4.
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" => 1424076 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "4" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/1-5" "field_display_title" => "1.5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1046 #items: array:1 [ 0 => App\Models\Branch {#1045 #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" => 1424064 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "I. Движение тел вблизи поверхности Земли и гравитация" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1047 #items: [] #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 {#1081 #items: array:1 [ 0 => App\Models\Book {#1048 #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" => 2549 "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 {#1050 #items: array:1 [ 0 => App\Models\Term {#1049 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #original: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1051 #items: array:1 [ 0 => App\Models\Term {#1052 #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 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "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 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "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 {#1053 #items: array:1 [ 0 => App\Models\Term {#1054 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #original: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1055 #items: array:3 [ 0 => App\Models\Term {#1056 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 3745 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Артеменков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Денис" "field_patronymic" => "Александрович" "field_surname_rp" => null ] #original: array:12 [ "id" => 3745 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Артеменков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Денис" "field_patronymic" => "Александрович" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1057 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 5014 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Ломаченков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Иван" "field_patronymic" => "Алексеевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 5014 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Ломаченков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Иван" "field_patronymic" => "Алексеевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Term {#1058 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 5412 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Панебратцев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Юрий" "field_patronymic" => "Анатольевич" "field_surname_rp" => "Панебратцева" ] #original: array:12 [ "id" => 5412 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Панебратцев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Юрий" "field_patronymic" => "Анатольевич" "field_surname_rp" => "Панебратцева" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1059 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1060 #items: array:1 [ 0 => App\Models\Term {#1061 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Задачник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "задачник" "field_creative_case" => "задачником" "field_dative_case" => "задачнику" "field_genitive_case" => "задачника" "field_nominative_case" => "задачник" "field_prepositional_case" => "задачнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "zadachnik" ] #original: array:10 [ "id" => 6518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Задачник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "задачник" "field_creative_case" => "задачником" "field_dative_case" => "задачнику" "field_genitive_case" => "задачника" "field_nominative_case" => "задачник" "field_prepositional_case" => "задачнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "zadachnik" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1062 #items: array:1 [ 0 => App\Models\Term {#1063 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "rossiya" ] #original: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "rossiya" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1064 #items: array:1 [ 0 => App\Models\Term {#1065 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "moskva" ] #original: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "moskva" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1066 #items: array:1 [ 0 => App\Models\Term {#1067 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:8 [ "id" => 4795 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "сферы" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "sfery" ] #original: array:8 [ "id" => 4795 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "сферы" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "sfery" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1068 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1069 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1070 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => "2" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1071 #items: array:1 [ 0 => App\Models\Term {#1072 #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" => 37 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "переработанное и дополненное" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "pererabotannoe i dopolnennoe" ] #original: array:6 [ "id" => 37 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "переработанное и дополненное" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "pererabotannoe i dopolnennoe" ] #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" => Illuminate\Database\Eloquent\Collection {#1073 #items: array:1 [ 0 => App\Models\Term {#1058} ] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2011" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "278" "field_priority" => null "field_default_folder" => "/fizika_09/artemenkov-z/" "field_isbn" => "978-5-09-038216-8" "field_cover" => array:1 [ 0 => "/media/fizika_09/artemenkov-z/covers/cover1.webp?ts=1758483621" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/artemenkov-z/covers/cover1.webp?ts=1758483621" "alt" => "" "width" => "1888" "height" => "2427" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1074 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1075 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1076 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1077 #items: array:1 [ 0 => App\Models\Term {#1078 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "siniy" ] #original: array:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "siniy" ] #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" => 2549 "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 {#1050} "field_class" => Illuminate\Database\Eloquent\Collection {#1051} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1053} "field_author" => Illuminate\Database\Eloquent\Collection {#1055} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1059} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1060} "field_country" => Illuminate\Database\Eloquent\Collection {#1062} "field_city" => Illuminate\Database\Eloquent\Collection {#1064} "field_series" => Illuminate\Database\Eloquent\Collection {#1066} "field_umk" => Illuminate\Database\Eloquent\Collection {#1068} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1069} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1070} "field_publication_number" => "2" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1071} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1073} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2011" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "278" "field_priority" => null "field_default_folder" => "/fizika_09/artemenkov-z/" "field_isbn" => "978-5-09-038216-8" "field_cover" => array:1 [ 0 => "/media/fizika_09/artemenkov-z/covers/cover1.webp?ts=1758483621" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/artemenkov-z/covers/cover1.webp?ts=1758483621" "alt" => "" "width" => "1888" "height" => "2427" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1074} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1075} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1076} "field_url" => "/9-klass/fizika/artemenkov-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1077} "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 {#1079 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1424064 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "I. Движение тел вблизи поверхности Земли и гравитация" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1047} "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 {#1081} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1079} ] #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 {#1038 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1034 #items: array:2 [ 0 => App\Models\Element {#1085 #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" => 1673694 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1094 #items: array:1 [ 0 => App\Models\Edition {#1086 #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" => 5990 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1088 #items: array:1 [ 0 => App\Models\Term {#1087 …30} ] #escapeWhenCastingToString: false } "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 {#1089 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1090 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1091 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 5990 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1088} "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 {#1089} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1090} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1091} "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" => "1424076" "type" => "task" ] "text" => "<p><strong>1.5</strong> Постройте график зависимости скорости от времени, если тело:</p><p><strong>1)</strong> из состояния покоя свободно падает вниз;</p><p><strong>2)</strong> падает вниз с начальной скоростью $10 \text{ м/с}$;</p><p><strong>3)</strong> брошено вертикально вверх с начальной скоростью $15 \text{ м/с}$.</p><p>Значение ускорения свободного падения принять равным $10 \text{ м/с}^2$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "5-1.jpg" "alt" => null "width" => "1738" "height" => 377 "path" => "/media/fizika_09/artemenkov-z/0-1/5-1.webp?ts=1758726356" ] ] ] #original: array:7 [ "id" => 1673694 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1094} "task" => array:2 [ "refs" => "1424076" "type" => "task" ] "text" => "<p><strong>1.5</strong> Постройте график зависимости скорости от времени, если тело:</p><p><strong>1)</strong> из состояния покоя свободно падает вниз;</p><p><strong>2)</strong> падает вниз с начальной скоростью $10 \text{ м/с}$;</p><p><strong>3)</strong> брошено вертикально вверх с начальной скоростью $15 \text{ м/с}$.</p><p>Значение ускорения свободного падения принять равным $10 \text{ м/с}^2$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "5-1.jpg" "alt" => null "width" => "1738" "height" => 377 "path" => "/media/fizika_09/artemenkov-z/0-1/5-1.webp?ts=1758726356" ] ] ] #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 {#1092 #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" => 1695236 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1102 #items: array:1 [ 0 => App\Models\Edition {#1093 #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" => 6166 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1096 #items: array:1 [ 0 => App\Models\Term {#1095 …30} ] #escapeWhenCastingToString: false } "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 {#1097 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1098 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1099 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6166 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1096} "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 {#1097} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1098} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1099} "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" => "1424076" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>$v_{01} = 0 \text{ м/с}$ (начальная скорость для случая 1)</p><p>$v_{02} = 10 \text{ м/с}$ (начальная скорость для случая 2)</p><p>$v_{03} = 15 \text{ м/с}$ (начальная скорость для случая 3)</p><p>$g = 10 \text{ м/с}^2$ (ускорение свободного падения)</p><p>Все величины представлены в Международной системе единиц (СИ).</p><p><strong>Найти:</strong></p><p>Построить графики зависимости скорости от времени $v(t)$ для трех заданных случаев.</p><p><strong>Решение:</strong></p><p>Для решения задачи выберем систему отсчета, связанную с Землей. Направим ось координат $OY$ вертикально вверх. В этом случае проекция ускорения свободного падения на ось $OY$ будет отрицательной, так как вектор ускорения $ \vec{g} $ направлен вниз: $a_y = -g = -10 \text{ м/с}^2$.</p><p>Зависимость проекции скорости от времени при равноускоренном движении описывается уравнением: $v_y(t) = v_{0y} + a_y t$, где $v_{0y}$ — проекция начальной скорости на ось $OY$.</p><p>Рассмотрим каждый случай.</p><p><strong>1)</strong> из состояния покоя свободно падает вниз</p><p>Тело падает из состояния покоя, это означает, что его начальная скорость равна нулю: $v_0 = 0$. Следовательно, проекция начальной скорости на ось $OY$ также равна нулю: $v_{0y} = 0$.</p><p>Подставим известные значения в уравнение скорости:</p><p>$v_y(t) = 0 + (-10) \cdot t = -10t$.</p><p>Это уравнение представляет собой линейную функцию. График зависимости $v_y(t)$ — это прямая линия, которая проходит через начало координат (точку (0; 0)) и имеет отрицательный наклон. Скорость направлена вниз (знак "минус") и её модуль линейно увеличивается со временем.</p><p><strong>Ответ:</strong> Уравнение зависимости скорости от времени: $v_y(t) = -10t$. Графиком является прямая линия, выходящая из начала координат и идущая вниз с угловым коэффициентом -10.</p><p><strong>2)</strong> падает вниз с начальной скоростью 10 м/с</p><p>Тело начинает падение с начальной скоростью $v_0 = 10 \text{ м/с}$, направленной вниз. Поскольку ось $OY$ направлена вверх, проекция начальной скорости на эту ось будет отрицательной: $v_{0y} = -10 \text{ м/с}$.</p><p>Подставим значения в уравнение скорости:</p><p>$v_y(t) = -10 + (-10) \cdot t = -10 - 10t$.</p><p>Графиком этой зависимости также является прямая линия. В начальный момент времени $t=0$ скорость тела $v_y(0) = -10 \text{ м/с}$. Это означает, что график начинается в точке (0; -10) на оси скоростей. Наклон прямой такой же, как и в первом случае, равен -10.</p><p><strong>Ответ:</strong> Уравнение зависимости скорости от времени: $v_y(t) = -10 - 10t$. Графиком является прямая линия, пересекающая ось скоростей в точке -10 м/с и идущая вниз.</p><p><strong>3)</strong> брошено вертикально вверх с начальной скоростью 15 м/с</p><p>Тело брошено вертикально вверх, значит, начальная скорость $v_0 = 15 \text{ м/с}$ направлена вверх. Её направление совпадает с направлением оси $OY$, поэтому проекция начальной скорости положительна: $v_{0y} = 15 \text{ м/с}$.</p><p>Подставим значения в уравнение скорости:</p><p>$v_y(t) = 15 + (-10) \cdot t = 15 - 10t$.</p><p>Графиком этой зависимости является прямая линия, которая в начальный момент времени $t=0$ пересекает ось скоростей в точке $v_y(0) = 15 \text{ м/с}$. Наклон прямой отрицателен и равен -10.</p><p>Тело будет двигаться вверх, пока его скорость не станет равной нулю. Найдем момент времени $t$, когда это произойдет (момент достижения максимальной высоты):</p><p>$0 = 15 - 10t$</p><p>$10t = 15$</p><p>$t = 1,5 \text{ с}$</p><p>Таким образом, график пересекает ось времени в точке $t = 1,5 \text{ с}$. Для $t > 1,5 \text{ с}$ скорость становится отрицательной, что означает, что тело начало двигаться вниз.</p><p><strong>Ответ:</strong> Уравнение зависимости скорости от времени: $v_y(t) = 15 - 10t$. Графиком является прямая линия, пересекающая ось скоростей в точке 15 м/с и ось времени в точке 1,5 с.</p>" ] #original: array:6 [ "id" => 1695236 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1102} "task" => array:2 [ "refs" => "1424076" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>$v_{01} = 0 \text{ м/с}$ (начальная скорость для случая 1)</p><p>$v_{02} = 10 \text{ м/с}$ (начальная скорость для случая 2)</p><p>$v_{03} = 15 \text{ м/с}$ (начальная скорость для случая 3)</p><p>$g = 10 \text{ м/с}^2$ (ускорение свободного падения)</p><p>Все величины представлены в Международной системе единиц (СИ).</p><p><strong>Найти:</strong></p><p>Построить графики зависимости скорости от времени $v(t)$ для трех заданных случаев.</p><p><strong>Решение:</strong></p><p>Для решения задачи выберем систему отсчета, связанную с Землей. Направим ось координат $OY$ вертикально вверх. В этом случае проекция ускорения свободного падения на ось $OY$ будет отрицательной, так как вектор ускорения $ \vec{g} $ направлен вниз: $a_y = -g = -10 \text{ м/с}^2$.</p><p>Зависимость проекции скорости от времени при равноускоренном движении описывается уравнением: $v_y(t) = v_{0y} + a_y t$, где $v_{0y}$ — проекция начальной скорости на ось $OY$.</p><p>Рассмотрим каждый случай.</p><p><strong>1)</strong> из состояния покоя свободно падает вниз</p><p>Тело падает из состояния покоя, это означает, что его начальная скорость равна нулю: $v_0 = 0$. Следовательно, проекция начальной скорости на ось $OY$ также равна нулю: $v_{0y} = 0$.</p><p>Подставим известные значения в уравнение скорости:</p><p>$v_y(t) = 0 + (-10) \cdot t = -10t$.</p><p>Это уравнение представляет собой линейную функцию. График зависимости $v_y(t)$ — это прямая линия, которая проходит через начало координат (точку (0; 0)) и имеет отрицательный наклон. Скорость направлена вниз (знак "минус") и её модуль линейно увеличивается со временем.</p><p><strong>Ответ:</strong> Уравнение зависимости скорости от времени: $v_y(t) = -10t$. Графиком является прямая линия, выходящая из начала координат и идущая вниз с угловым коэффициентом -10.</p><p><strong>2)</strong> падает вниз с начальной скоростью 10 м/с</p><p>Тело начинает падение с начальной скоростью $v_0 = 10 \text{ м/с}$, направленной вниз. Поскольку ось $OY$ направлена вверх, проекция начальной скорости на эту ось будет отрицательной: $v_{0y} = -10 \text{ м/с}$.</p><p>Подставим значения в уравнение скорости:</p><p>$v_y(t) = -10 + (-10) \cdot t = -10 - 10t$.</p><p>Графиком этой зависимости также является прямая линия. В начальный момент времени $t=0$ скорость тела $v_y(0) = -10 \text{ м/с}$. Это означает, что график начинается в точке (0; -10) на оси скоростей. Наклон прямой такой же, как и в первом случае, равен -10.</p><p><strong>Ответ:</strong> Уравнение зависимости скорости от времени: $v_y(t) = -10 - 10t$. Графиком является прямая линия, пересекающая ось скоростей в точке -10 м/с и идущая вниз.</p><p><strong>3)</strong> брошено вертикально вверх с начальной скоростью 15 м/с</p><p>Тело брошено вертикально вверх, значит, начальная скорость $v_0 = 15 \text{ м/с}$ направлена вверх. Её направление совпадает с направлением оси $OY$, поэтому проекция начальной скорости положительна: $v_{0y} = 15 \text{ м/с}$.</p><p>Подставим значения в уравнение скорости:</p><p>$v_y(t) = 15 + (-10) \cdot t = 15 - 10t$.</p><p>Графиком этой зависимости является прямая линия, которая в начальный момент времени $t=0$ пересекает ось скоростей в точке $v_y(0) = 15 \text{ м/с}$. Наклон прямой отрицателен и равен -10.</p><p>Тело будет двигаться вверх, пока его скорость не станет равной нулю. Найдем момент времени $t$, когда это произойдет (момент достижения максимальной высоты):</p><p>$0 = 15 - 10t$</p><p>$10t = 15$</p><p>$t = 1,5 \text{ с}$</p><p>Таким образом, график пересекает ось времени в точке $t = 1,5 \text{ с}$. Для $t > 1,5 \text{ с}$ скорость становится отрицательной, что означает, что тело начало двигаться вниз.</p><p><strong>Ответ:</strong> Уравнение зависимости скорости от времени: $v_y(t) = 15 - 10t$. Графиком является прямая линия, пересекающая ось скоростей в точке 15 м/с и ось времени в точке 1,5 с.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1424077" "type" => "task" ] "previous" => array:2 [ "refs" => "1424075" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1082 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1043 #items: array:1 [ 0 => App\Models\BookPage {#1080 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false 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"elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1674164 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1114 #items: array:1 [ 0 => App\Models\Edition {#1086} ] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1424354" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "4-1.jpg" "alt" => null "width" => "1994" "height" => 2505 "path" => "/media/fizika_09/artemenkov-z/0-1/4-1.webp?ts=1758727968" ] ] ] #original: array:6 [ "id" => 1674164 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1114} "book_page" => array:2 [ "refs" => "1424354" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "4-1.jpg" "alt" => null "width" => "1994" "height" => 2505 "path" => "/media/fizika_09/artemenkov-z/0-1/4-1.webp?ts=1758727968" ] ] ] #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" => "1424355" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1424353" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1168 #items: array:9 [ 0 => App\Models\Task {#1184 #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" => 1424072 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "4" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/1-1" "field_display_title" => "1.1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1185 #items: array:1 [ 0 => App\Models\Term {#1036} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1186 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1187 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1188 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection 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"edition_groups" => Illuminate\Database\Eloquent\Collection {#1186} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1187} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1188} "content" => Illuminate\Database\Eloquent\Collection {#1190} "next" => array:2 [ "refs" => "1424073" "type" => "task" ] "previous" => array:2 [ "refs" => null "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1196} "page" => array:2 [ "refs" => "1424354" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Task {#1191 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true 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Illuminate\Database\Eloquent\Collection {#1192 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1193 #items: array:2 [ 0 => App\Models\Element {#1211 …30} 1 => App\Models\Element {#1213 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1424074" "type" => "task" ] "previous" => array:2 [ "refs" => "1424072" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1208 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1424354" "type" => "book_page" ] ] #original: array:24 [ "id" => 1424073 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "4" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/1-2" "field_display_title" => "1.2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1189} 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App\Models\Task {#1203 #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" => 1424074 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "4" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/1-3" "field_display_title" => "1.3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1195 #items: array:1 [ 0 => App\Models\Term {#1036} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1210 #items: [] #escapeWhenCastingToString: false } 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"/9-klass/fizika/artemenkov-zadachnik/1-3" "field_display_title" => "1.3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1195} "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 {#1210} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1206} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1204} "content" => Illuminate\Database\Eloquent\Collection {#1205} "next" => array:2 [ "refs" => "1424075" "type" => "task" ] "previous" => array:2 [ "refs" => "1424073" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1220} "page" => array:2 [ "refs" => "1424354" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Task {#1215 #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" => 1424075 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "4" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/1-4" "field_display_title" => "1.4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1207 #items: array:1 [ 0 => App\Models\Term {#1036} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1222 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1218 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1216 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1217 #items: array:2 [ 0 => App\Models\Element {#1235 …30} 1 => App\Models\Element {#1237 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1424076" "type" => "task" ] "previous" => array:2 [ "refs" => "1424074" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1232 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1424354" "type" => "book_page" ] ] #original: array:24 [ "id" => 1424075 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "4" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/1-4" "field_display_title" => "1.4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1207} "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 {#1222} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1218} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1216} "content" => Illuminate\Database\Eloquent\Collection {#1217} "next" => array:2 [ "refs" => "1424076" "type" => "task" ] "previous" => array:2 [ "refs" => "1424074" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1232} "page" => array:2 [ "refs" => "1424354" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 4 => App\Models\Task {#1227 #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" => 1424076 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "4" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/1-5" "field_display_title" => "1.5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1219 #items: array:1 [ 0 => App\Models\Term {#1036} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1234 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1230 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1228 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1231 #items: array:2 [ 0 => App\Models\Element {#1085} 1 => App\Models\Element {#1092} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1424077" "type" => "task" ] "previous" => array:2 [ "refs" => "1424075" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1229 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1424354" "type" => "book_page" ] ] #original: array:24 [ "id" => 1424076 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "4" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/1-5" "field_display_title" => "1.5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1219} "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 {#1234} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1230} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1228} "content" => Illuminate\Database\Eloquent\Collection {#1231} "next" => array:2 [ "refs" => "1424077" "type" => "task" ] "previous" => array:2 [ "refs" => "1424075" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1229} "page" => array:2 [ "refs" => "1424354" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 5 => App\Models\Task {#1239 #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" => 1424077 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "4" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/1-6" "field_display_title" => "1.6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1240 #items: array:1 [ 0 => App\Models\Term {#1036} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1241 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1242 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1243 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1245 #items: array:2 [ 0 => App\Models\Element {#1254 …30} 1 => App\Models\Element {#1256 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1424078" "type" => "task" ] "previous" => array:2 [ "refs" => "1424076" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1251 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1424354" "type" => "book_page" ] ] #original: array:24 [ "id" => 1424077 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "4" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/1-6" "field_display_title" => "1.6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1240} "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 {#1241} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1242} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1243} "content" => Illuminate\Database\Eloquent\Collection {#1245} "next" => array:2 [ "refs" => "1424078" "type" => "task" ] "previous" => array:2 [ "refs" => "1424076" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1251} "page" => array:2 [ "refs" => "1424354" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 6 => App\Models\Task {#1246 #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" => 1424078 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "4" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/1-7" "field_display_title" => "1.7" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1244 #items: array:1 [ 0 => App\Models\Term {#1036} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1253 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1249 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1247 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1248 #items: array:2 [ 0 => App\Models\Element {#1266 …30} 1 => App\Models\Element {#1268 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1424079" "type" => "task" ] "previous" => array:2 [ "refs" => "1424077" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1263 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1424354" "type" => "book_page" ] ] #original: array:24 [ "id" => 1424078 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "4" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/1-7" "field_display_title" => "1.7" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1244} "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 {#1253} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1249} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1247} "content" => Illuminate\Database\Eloquent\Collection {#1248} "next" => array:2 [ "refs" => "1424079" "type" => "task" ] "previous" => array:2 [ "refs" => "1424077" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1263} "page" => array:2 [ "refs" => "1424354" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 7 => App\Models\Task {#1258 #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" => 1424079 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "4" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/1-8" "field_display_title" => "1.8" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1250 #items: array:1 [ 0 => App\Models\Term {#1036} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1265 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1261 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1259 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1260 #items: array:2 [ 0 => App\Models\Element {#1278 …30} 1 => App\Models\Element {#1280 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1424080" "type" => "task" ] "previous" => array:2 [ "refs" => "1424078" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1275 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1424354" "type" => "book_page" ] ] #original: array:24 [ "id" => 1424079 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "4" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/1-8" "field_display_title" => "1.8" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1250} "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 {#1265} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1261} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1259} "content" => Illuminate\Database\Eloquent\Collection {#1260} "next" => array:2 [ "refs" => "1424080" "type" => "task" ] "previous" => array:2 [ "refs" => "1424078" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1275} "page" => array:2 [ "refs" => "1424354" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 8 => App\Models\Task {#1270 #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" => 1424080 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "4" "field_page_end" => "5" "field_url" => "/9-klass/fizika/artemenkov-zadachnik/1-9" "field_display_title" => "1.9" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1262 #items: array:1 [ 0 => App\Models\Term {#1036} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1277 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1273 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1271 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1272 #items: array:2 [ 0 => App\Models\Element {#1290 …30} 1 => App\Models\Element {#1292 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1424081" "type" => "task" ] "previous" => array:2 [ "refs" => "1424079" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1287 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1424354" "type" => "book_page" ] ] #original: array:24 [ "id" => 1424080 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "4" "field_page_end" => "5" "field_url" => "/9-klass/fizika/artemenkov-zadachnik/1-9" "field_display_title" => "1.9" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1262} "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 {#1277} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1273} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1271} "content" => Illuminate\Database\Eloquent\Collection {#1272} "next" => array:2 [ "refs" => "1424081" "type" => "task" ] "previous" => array:2 [ "refs" => "1424079" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1287} "page" => array:2 [ "refs" => "1424354" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1424354 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "4" "field_url" => "/9-klass/fizika/artemenkov-zadachnik/page-4" "field_display_title" => "4" "field_folder" => "1" "field_image_name" => "4" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1100} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1101} "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 {#1103} "content" => Illuminate\Database\Eloquent\Collection {#1113} "next" => array:2 [ "refs" => "1424355" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1424353" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1168} ] #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" => 1424076 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "4" "field_page_end" => null "field_url" => "/9-klass/fizika/artemenkov-zadachnik/1-5" "field_display_title" => "1.5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1046} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1038} "content" => Illuminate\Database\Eloquent\Collection {#1034} "next" => array:2 [ "refs" => "1424077" "type" => "task" ] "previous" => array:2 [ "refs" => "1424075" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1082} "page" => array:2 [ "refs" => "1424354" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
№1.5 (с. 4)
Условие. №1.5 (с. 4)
скриншот условия
1.5 Постройте график зависимости скорости от времени, если тело:
1) из состояния покоя свободно падает вниз;
2) падает вниз с начальной скоростью $10 \text{ м/с}$;
3) брошено вертикально вверх с начальной скоростью $15 \text{ м/с}$.
Значение ускорения свободного падения принять равным $10 \text{ м/с}^2$.
Решение. №1.5 (с. 4)
Дано:
$v_{01} = 0 \text{ м/с}$ (начальная скорость для случая 1)
$v_{02} = 10 \text{ м/с}$ (начальная скорость для случая 2)
$v_{03} = 15 \text{ м/с}$ (начальная скорость для случая 3)
$g = 10 \text{ м/с}^2$ (ускорение свободного падения)
Все величины представлены в Международной системе единиц (СИ).
Найти:
Построить графики зависимости скорости от времени $v(t)$ для трех заданных случаев.
Решение:
Для решения задачи выберем систему отсчета, связанную с Землей. Направим ось координат $OY$ вертикально вверх. В этом случае проекция ускорения свободного падения на ось $OY$ будет отрицательной, так как вектор ускорения $ \vec{g} $ направлен вниз: $a_y = -g = -10 \text{ м/с}^2$.
Зависимость проекции скорости от времени при равноускоренном движении описывается уравнением: $v_y(t) = v_{0y} + a_y t$, где $v_{0y}$ — проекция начальной скорости на ось $OY$.
Рассмотрим каждый случай.
1) из состояния покоя свободно падает вниз
Тело падает из состояния покоя, это означает, что его начальная скорость равна нулю: $v_0 = 0$. Следовательно, проекция начальной скорости на ось $OY$ также равна нулю: $v_{0y} = 0$.
Подставим известные значения в уравнение скорости:
$v_y(t) = 0 + (-10) \cdot t = -10t$.
Это уравнение представляет собой линейную функцию. График зависимости $v_y(t)$ — это прямая линия, которая проходит через начало координат (точку (0; 0)) и имеет отрицательный наклон. Скорость направлена вниз (знак "минус") и её модуль линейно увеличивается со временем.
Ответ: Уравнение зависимости скорости от времени: $v_y(t) = -10t$. Графиком является прямая линия, выходящая из начала координат и идущая вниз с угловым коэффициентом -10.
2) падает вниз с начальной скоростью 10 м/с
Тело начинает падение с начальной скоростью $v_0 = 10 \text{ м/с}$, направленной вниз. Поскольку ось $OY$ направлена вверх, проекция начальной скорости на эту ось будет отрицательной: $v_{0y} = -10 \text{ м/с}$.
Подставим значения в уравнение скорости:
$v_y(t) = -10 + (-10) \cdot t = -10 - 10t$.
Графиком этой зависимости также является прямая линия. В начальный момент времени $t=0$ скорость тела $v_y(0) = -10 \text{ м/с}$. Это означает, что график начинается в точке (0; -10) на оси скоростей. Наклон прямой такой же, как и в первом случае, равен -10.
Ответ: Уравнение зависимости скорости от времени: $v_y(t) = -10 - 10t$. Графиком является прямая линия, пересекающая ось скоростей в точке -10 м/с и идущая вниз.
3) брошено вертикально вверх с начальной скоростью 15 м/с
Тело брошено вертикально вверх, значит, начальная скорость $v_0 = 15 \text{ м/с}$ направлена вверх. Её направление совпадает с направлением оси $OY$, поэтому проекция начальной скорости положительна: $v_{0y} = 15 \text{ м/с}$.
Подставим значения в уравнение скорости:
$v_y(t) = 15 + (-10) \cdot t = 15 - 10t$.
Графиком этой зависимости является прямая линия, которая в начальный момент времени $t=0$ пересекает ось скоростей в точке $v_y(0) = 15 \text{ м/с}$. Наклон прямой отрицателен и равен -10.
Тело будет двигаться вверх, пока его скорость не станет равной нулю. Найдем момент времени $t$, когда это произойдет (момент достижения максимальной высоты):
$0 = 15 - 10t$
$10t = 15$
$t = 1,5 \text{ с}$
Таким образом, график пересекает ось времени в точке $t = 1,5 \text{ с}$. Для $t > 1,5 \text{ с}$ скорость становится отрицательной, что означает, что тело начало двигаться вниз.
Ответ: Уравнение зависимости скорости от времени: $v_y(t) = 15 - 10t$. Графиком является прямая линия, пересекающая ось скоростей в точке 15 м/с и ось времени в точке 1,5 с.
Другие задания:
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