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Номер 2.2, страница 16 - гдз по физике 10-11 класс задачник Гельфгат, Генденштейн
Авторы: Гельфгат И. М., Генденштейн Л. Э., Кирик Л. А.
Тип: Задачник
Издательство: Илекса
Год издания: 2008 - 2026
Уровень обучения: профильный
Цвет обложки: красный лупа, парень едет на велосипеде
ISBN: 978-5-89237-252-7
Популярные ГДЗ в 10 классе
Механика. Кинематика. 2. Прямолинейное равноускоренное движение. Упражнения - номер 2.2, 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" => 1319409 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "16" "field_page_end" => null "field_url" => "/10-klass/fizika/gelfgat-zadachnik/02-2" "field_display_title" => "2.2" "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" => 1319266 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1047 #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 {#1057 #items: array:1 [ 0 => App\Models\Book {#1056 #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" => 5400 "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 {#1061 #items: array:1 [ 0 => 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: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 {#1059 #items: array:2 [ 0 => App\Models\Term {#1070 #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" => 5459 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "10" "field_cases" => array:6 [ "field_accusative_case" => "десятый" "field_creative_case" => "десятым" "field_dative_case" => "десятому" "field_genitive_case" => "десятого" "field_nominative_case" => "десятый" "field_prepositional_case" => "десятом" ] "field_translit" => "desjatyj" ] #original: array:6 [ "id" => 5459 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "10" "field_cases" => array:6 [ "field_accusative_case" => "десятый" "field_creative_case" => "десятым" "field_dative_case" => "десятому" "field_genitive_case" => "десятого" "field_nominative_case" => "десятый" "field_prepositional_case" => "десятом" ] "field_translit" => "desjatyj" ] #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 {#1071 #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" => 5460 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "11" "field_cases" => array:6 [ "field_accusative_case" => "одиннадцатый" "field_creative_case" => "одиннадцатым" "field_dative_case" => "одиннадцатому" "field_genitive_case" => "одинадцатого" "field_nominative_case" => "одинадцатый" "field_prepositional_case" => "одиннадцатом" ] "field_translit" => "odinadcatyj" ] #original: array:6 [ "id" => 5460 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "11" "field_cases" => array:6 [ "field_accusative_case" => "одиннадцатый" "field_creative_case" => "одиннадцатым" "field_dative_case" => "одиннадцатому" "field_genitive_case" => "одинадцатого" "field_nominative_case" => "одинадцатый" "field_prepositional_case" => "одиннадцатом" ] "field_translit" => "odinadcatyj" ] #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 {#1069 #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:6 [ "id" => 5158 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Илекса" "field_cases" => null "field_translit" => "ileksa" ] #original: array:6 [ "id" => 5158 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Илекса" "field_cases" => null "field_translit" => "ileksa" ] #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 {#1065 #items: array:3 [ 0 => App\Models\Term {#1077 #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" => 4102 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Гельфгат" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Илья" "field_patronymic" => "Маркович" "field_surname_rp" => null ] #original: array:12 [ "id" => 4102 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Гельфгат" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Илья" "field_patronymic" => "Маркович" "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 {#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: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 => "*" ] } 2 => App\Models\Term {#1079 #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" => 4583 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кирик" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Леонид" "field_patronymic" => "Анатольевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4583 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кирик" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Леонид" "field_patronymic" => "Анатольевич" "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 {#1074 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1075 #items: array:1 [ 0 => App\Models\Term {#1062 #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 {#1063 #items: array:1 [ 0 => App\Models\Term {#1073 #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 {#1066 #items: array:1 [ 0 => App\Models\Term {#1064 #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 {#1072 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1060 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1089 #items: array:1 [ 0 => App\Models\Term {#1088 #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" => 40 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "профильный" "field_cases" => array:6 [ "field_accusative_case" => "профильный" "field_creative_case" => "профильным" "field_dative_case" => "профильному" "field_genitive_case" => "профильного" "field_nominative_case" => "профильный" "field_prepositional_case" => "профильном" ] "field_translit" => "profilnyy" ] #original: array:6 [ "id" => 40 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "профильный" "field_cases" => array:6 [ "field_accusative_case" => "профильный" "field_creative_case" => "профильным" "field_dative_case" => "профильному" "field_genitive_case" => "профильного" "field_nominative_case" => "профильный" "field_prepositional_case" => "профильном" ] "field_translit" => "profilnyy" ] #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_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1081 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1082 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1080 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "лупа, парень едет на велосипеде" "field_publication_year" => "2008" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "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" => "459" "field_priority" => null "field_default_folder" => "/fizika_10/gelfgat-z/" "field_isbn" => "978-5-89237-252-7" "field_cover" => array:1 [ 0 => "/media/fizika_10/gelfgat-z/covers/cover1.webp?ts=1756049816" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_10/gelfgat-z/covers/cover1.webp?ts=1756049816" "alt" => "" "width" => "1566" "height" => "2412" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1085 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1083 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1086 #items: [] #escapeWhenCastingToString: false } "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1098 #items: array:1 [ 0 => App\Models\Term {#1097 #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" => 46 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "красный" "field_cases" => array:6 [ "field_accusative_case" => "красный" "field_creative_case" => "красным" "field_dative_case" => "красному" "field_genitive_case" => "красного" "field_nominative_case" => "красный" "field_prepositional_case" => "красном" ] "field_translit" => "krasnyy" ] #original: array:6 [ "id" => 46 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "красный" "field_cases" => array:6 [ "field_accusative_case" => "красный" "field_creative_case" => "красным" "field_dative_case" => "красному" "field_genitive_case" => "красного" "field_nominative_case" => "красный" "field_prepositional_case" => "красном" ] "field_translit" => "krasnyy" ] #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" => 381 "subject" => 556 "class_subject" => 494 ] ] #original: array:50 [ "id" => 5400 "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 {#1061} "field_class" => Illuminate\Database\Eloquent\Collection {#1059} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1069} "field_author" => Illuminate\Database\Eloquent\Collection {#1065} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1074} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1075} "field_country" => Illuminate\Database\Eloquent\Collection {#1063} "field_city" => Illuminate\Database\Eloquent\Collection {#1066} "field_series" => Illuminate\Database\Eloquent\Collection {#1072} "field_umk" => Illuminate\Database\Eloquent\Collection {#1060} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1089} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1081} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1082} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1080} "field_under_the_edition_degree" => null "field_cover_description" => "лупа, парень едет на велосипеде" "field_publication_year" => "2008" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "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" => "459" "field_priority" => null "field_default_folder" => "/fizika_10/gelfgat-z/" "field_isbn" => "978-5-89237-252-7" "field_cover" => array:1 [ 0 => "/media/fizika_10/gelfgat-z/covers/cover1.webp?ts=1756049816" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_10/gelfgat-z/covers/cover1.webp?ts=1756049816" "alt" => "" "width" => "1566" "height" => "2412" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1085} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1083} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1086} "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1098} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 381 "subject" => 556 "class_subject" => 494 ] ] #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 {#1049 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319266 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1047} "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 {#1057} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1049} ] #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 {#1116 #items: array:4 [ 0 => App\Models\Branch {#1126 #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" => 1319266 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1127 #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 {#1128 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1129 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319266 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Механика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1127} "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 {#1128} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1129} ] #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 {#1130 #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" => 1319267 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Кинематика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1131 #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 {#1132 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1133 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319267 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Кинематика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1131} "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 {#1132} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1133} ] #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 {#1134 #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" => 1319271 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "2. Прямолинейное равноускоренное движение" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1135 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "16" "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 {#1136 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1145 #items: array:1 [ 0 => App\Models\Branch {#1144 #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" => 1319267 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Кинематика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1146 #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 {#1147 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1148 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319267 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Кинематика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1146} "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 {#1147} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1148} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319271 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "2. Прямолинейное равноускоренное движение" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1135} "field_page_start" => "16" "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 {#1136} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1145} ] #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 {#1138 #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" => 1319272 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Упражнения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1137 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "16" "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 {#1141 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1154 #items: array:1 [ 0 => App\Models\Branch {#1153 #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" => 1319271 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "2. Прямолинейное равноускоренное движение" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1155 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "16" "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 {#1156 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1157 #items: array:1 [ 0 => App\Models\Branch {#1144} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319271 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "2. Прямолинейное равноускоренное движение" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1155} "field_page_start" => "16" "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 {#1156} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1157} ] #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" => 1319272 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Упражнения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1137} "field_page_start" => "16" "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 {#1141} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1154} ] #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 {#1038 #items: array:2 [ 0 => App\Models\Element {#1107 #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" => 1493690 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1095 #items: array:1 [ 0 => App\Models\Edition {#1106 #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" => 5430 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1103 #items: array:1 [ 0 => App\Models\Term {#1105 #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" => 5158 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Илекса" "field_cases" => null "field_translit" => "ileksa" ] #original: array:6 [ "id" => 5158 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Илекса" "field_cases" => null "field_translit" => "ileksa" ] #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_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 {#1104 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1102 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1101 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 5430 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1103} "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 {#1104} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1102} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1101} "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" => "1319409" "type" => "task" ] "text" => "<p><strong>2.2.</strong> От толчка шарик вкатывается на наклонную плоскость. На расстоянии $l = 30$ см от начала движения шарик побывал дважды: через $t_1 = 1$ с и $t_2 = 2$ с после толчка. Считая движение равноускоренным, найдите начальную скорость $v_0$ и ускорение $\text{a}$.</p><p></p><p>☑ $45 \frac{см} {с}$ $30 \frac{см} {с^2}$.</p><p><strong><em>Решение.</em></strong> Зависимость координаты шарика от времени выражается формулой $x = v_{0x}t - \frac{a_x t^2}{2}$. Отсюда получаем квадратное уравнение $t^2 - \frac{2v_{0x}}{a_x}t + \frac{2x}{a_x} = 0$. Так как $t_1$ и $t_2$ — корни этого уравнения при $x = l$, то согласно теореме Виета $t_1 + t_2 = \frac{2v_{0x}}{a_x}$ и $t_1 t_2 = \frac{2l}{a_x}$. Из полученной системы уравнений находим: $a_x = \frac{2l}{t_1 t_2} = 30 \text{ (см/с}^2\text{)}$, $v_{0x} = \frac{(t_1 + t_2) \cdot a_x}{2} = 45 \text{ (см/с)}$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "1471" "height" => 1129 "path" => "/media/fizika_10/gelfgat-z/0-02/2-1.webp?ts=1756251003" ] ] ] #original: array:7 [ "id" => 1493690 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1095} "task" => array:2 [ "refs" => "1319409" "type" => "task" ] "text" => "<p><strong>2.2.</strong> От толчка шарик вкатывается на наклонную плоскость. На расстоянии $l = 30$ см от начала движения шарик побывал дважды: через $t_1 = 1$ с и $t_2 = 2$ с после толчка. Считая движение равноускоренным, найдите начальную скорость $v_0$ и ускорение $\text{a}$.</p><p></p><p>☑ $45 \frac{см} {с}$ $30 \frac{см} {с^2}$.</p><p><strong><em>Решение.</em></strong> Зависимость координаты шарика от времени выражается формулой $x = v_{0x}t - \frac{a_x t^2}{2}$. Отсюда получаем квадратное уравнение $t^2 - \frac{2v_{0x}}{a_x}t + \frac{2x}{a_x} = 0$. Так как $t_1$ и $t_2$ — корни этого уравнения при $x = l$, то согласно теореме Виета $t_1 + t_2 = \frac{2v_{0x}}{a_x}$ и $t_1 t_2 = \frac{2l}{a_x}$. Из полученной системы уравнений находим: $a_x = \frac{2l}{t_1 t_2} = 30 \text{ (см/с}^2\text{)}$, $v_{0x} = \frac{(t_1 + t_2) \cdot a_x}{2} = 45 \text{ (см/с)}$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "1471" "height" => 1129 "path" => "/media/fizika_10/gelfgat-z/0-02/2-1.webp?ts=1756251003" ] ] ] #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 {#1099 #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" => 1691247 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1052 #items: array:1 [ 0 => App\Models\Edition {#1100 #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" => 6138 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1094 #items: array:1 [ 0 => App\Models\Term {#1093 #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" => 7012 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Gemini 2.5 Pro" "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" => "gemini 2.5 pro" ] #original: array:6 [ "id" => 7012 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Gemini 2.5 Pro" "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" => "gemini 2.5 pro" ] #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_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 {#1092 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1084 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1054 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6138 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1094} "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 {#1092} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1084} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1054} "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" => "1319409" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>$l = 30 \text{ см}$</p><p>$t_1 = 1 \text{ с}$</p><p>$t_2 = 2 \text{ с}$</p><p>Перевод в систему СИ:</p><p>$l = 30 \text{ см} = 0.3 \text{ м}$</p><p><strong>Найти:</strong></p><p>$v_0$ - начальная скорость</p><p>$a$ - ускорение</p><p><strong>Решение:</strong></p><p>Движение шарика по наклонной плоскости является равноускоренным. Зависимость координаты шарика $x$ от времени $t$ описывается уравнением:</p><p>$x(t) = v_0 t + \frac{at^2}{2}$</p><p>где $v_0$ — начальная скорость, а $a$ — ускорение. Поскольку шарик вкатывается на наклонную плоскость, его скорость уменьшается, следовательно, вектор ускорения направлен против вектора начальной скорости, и проекция ускорения на ось движения будет отрицательной.</p><p>По условию задачи, в моменты времени $t_1$ и $t_2$ шарик находится на одном и том же расстоянии $l$ от начала движения. Это означает, что $t_1$ и $t_2$ являются корнями уравнения $l = v_0 t + \frac{at^2}{2}$ относительно времени $t$.</p><p>Перепишем это уравнение в виде стандартного квадратного уравнения относительно $t$ ($At^2 + Bt + C = 0$):</p><p>$\frac{a}{2}t^2 + v_0 t - l = 0$</p><p>Согласно теореме Виета, для квадратного уравнения сумма корней равна $-B/A$, а произведение корней равно $C/A$.</p><p>В нашем случае коэффициенты равны: $A = \frac{a}{2}$, $B = v_0$, $C = -l$.</p><p>Применим теорему Виета к нашему уравнению:</p><p>Сумма корней: $t_1 + t_2 = -\frac{v_0}{a/2} = -\frac{2v_0}{a}$</p><p>Произведение корней: $t_1 t_2 = \frac{-l}{a/2} = -\frac{2l}{a}$</p><p>Мы получили систему из двух уравнений с двумя неизвестными $v_0$ и $a$:</p><p>$\begin{cases} t_1 + t_2 = -2v_0/a \\ t_1 t_2 = -2l/a \end{cases}$</p><p>Из второго уравнения выразим ускорение $a$:</p><p>$a = -\frac{2l}{t_1 t_2}$</p><p>Из первого уравнения выразим начальную скорость $v_0$:</p><p>$v_0 = -\frac{a(t_1 + t_2)}{2}$</p><p>Подставим известные значения (для удобства будем производить вычисления в исходных единицах, см и с):</p><p>$l = 30 \text{ см}$, $t_1 = 1 \text{ с}$, $t_2 = 2 \text{ с}$.</p><p>Найдем ускорение:</p><p>$a = -\frac{2 \cdot 30 \text{ см}}{1 \text{ с} \cdot 2 \text{ с}} = -\frac{60 \text{ см}}{2 \text{ с}^2} = -30 \text{ см/с}^2$</p><p>Теперь найдем начальную скорость:</p><p>$v_0 = -\frac{(-30 \text{ см/с}^2) \cdot (1 \text{ с} + 2 \text{ с})}{2} = -\frac{(-30 \text{ см/с}^2) \cdot 3 \text{ с}}{2} = \frac{90 \text{ см/с}}{2} = 45 \text{ см/с}$</p><p>Таким образом, начальная скорость шарика равна 45 см/с, а его ускорение равно -30 см/с². Отрицательный знак ускорения подтверждает, что движение является равнозамедленным.</p><p><strong>Ответ:</strong> начальная скорость $v_0 = 45 \text{ см/с}$; ускорение $a = -30 \text{ см/с}^2$ (модуль ускорения равен $30 \text{ см/с}^2$).</p>" ] #original: array:6 [ "id" => 1691247 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1052} "task" => array:2 [ "refs" => "1319409" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>$l = 30 \text{ см}$</p><p>$t_1 = 1 \text{ с}$</p><p>$t_2 = 2 \text{ с}$</p><p>Перевод в систему СИ:</p><p>$l = 30 \text{ см} = 0.3 \text{ м}$</p><p><strong>Найти:</strong></p><p>$v_0$ - начальная скорость</p><p>$a$ - ускорение</p><p><strong>Решение:</strong></p><p>Движение шарика по наклонной плоскости является равноускоренным. Зависимость координаты шарика $x$ от времени $t$ описывается уравнением:</p><p>$x(t) = v_0 t + \frac{at^2}{2}$</p><p>где $v_0$ — начальная скорость, а $a$ — ускорение. Поскольку шарик вкатывается на наклонную плоскость, его скорость уменьшается, следовательно, вектор ускорения направлен против вектора начальной скорости, и проекция ускорения на ось движения будет отрицательной.</p><p>По условию задачи, в моменты времени $t_1$ и $t_2$ шарик находится на одном и том же расстоянии $l$ от начала движения. Это означает, что $t_1$ и $t_2$ являются корнями уравнения $l = v_0 t + \frac{at^2}{2}$ относительно времени $t$.</p><p>Перепишем это уравнение в виде стандартного квадратного уравнения относительно $t$ ($At^2 + Bt + C = 0$):</p><p>$\frac{a}{2}t^2 + v_0 t - l = 0$</p><p>Согласно теореме Виета, для квадратного уравнения сумма корней равна $-B/A$, а произведение корней равно $C/A$.</p><p>В нашем случае коэффициенты равны: $A = \frac{a}{2}$, $B = v_0$, $C = -l$.</p><p>Применим теорему Виета к нашему уравнению:</p><p>Сумма корней: $t_1 + t_2 = -\frac{v_0}{a/2} = -\frac{2v_0}{a}$</p><p>Произведение корней: $t_1 t_2 = \frac{-l}{a/2} = -\frac{2l}{a}$</p><p>Мы получили систему из двух уравнений с двумя неизвестными $v_0$ и $a$:</p><p>$\begin{cases} t_1 + t_2 = -2v_0/a \\ t_1 t_2 = -2l/a \end{cases}$</p><p>Из второго уравнения выразим ускорение $a$:</p><p>$a = -\frac{2l}{t_1 t_2}$</p><p>Из первого уравнения выразим начальную скорость $v_0$:</p><p>$v_0 = -\frac{a(t_1 + t_2)}{2}$</p><p>Подставим известные значения (для удобства будем производить вычисления в исходных единицах, см и с):</p><p>$l = 30 \text{ см}$, $t_1 = 1 \text{ с}$, $t_2 = 2 \text{ с}$.</p><p>Найдем ускорение:</p><p>$a = -\frac{2 \cdot 30 \text{ см}}{1 \text{ с} \cdot 2 \text{ с}} = -\frac{60 \text{ см}}{2 \text{ с}^2} = -30 \text{ см/с}^2$</p><p>Теперь найдем начальную скорость:</p><p>$v_0 = -\frac{(-30 \text{ см/с}^2) \cdot (1 \text{ с} + 2 \text{ с})}{2} = -\frac{(-30 \text{ см/с}^2) \cdot 3 \text{ с}}{2} = \frac{90 \text{ см/с}}{2} = 45 \text{ см/с}$</p><p>Таким образом, начальная скорость шарика равна 45 см/с, а его ускорение равно -30 см/с². Отрицательный знак ускорения подтверждает, что движение является равнозамедленным.</p><p><strong>Ответ:</strong> начальная скорость $v_0 = 45 \text{ см/с}$; ускорение $a = -30 \text{ см/с}^2$ (модуль ускорения равен $30 \text{ см/с}^2$).</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" => "1319410" "type" => "task" ] "previous" => array:2 [ "refs" => "1319408" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1110 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1042 #items: array:1 [ 0 => App\Models\BookPage {#1112 #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" => 1340977 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "16" "field_url" => "/10-klass/fizika/gelfgat-zadachnik/page-16" "field_display_title" => "16" "field_folder" => "1" "field_image_name" => "16" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1091 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1090 #items: array:1 [ 0 => App\Models\Book {#1056} ] #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 {#1053 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1122 #items: array:1 [ 0 => App\Models\Element {#1114 #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" => 1519522 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1121 #items: array:1 [ 0 => App\Models\Edition {#1106} ] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1340977" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "16-1.jpg" "alt" => null "width" => "1536" "height" => 2444 "path" => "/media/fizika_10/gelfgat-z/0-1/16-1.webp?ts=1756642280" ] ] ] #original: array:6 [ "id" => 1519522 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1121} "book_page" => array:2 [ "refs" => "1340977" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "16-1.jpg" "alt" => null "width" => "1536" "height" => 2444 "path" => "/media/fizika_10/gelfgat-z/0-1/16-1.webp?ts=1756642280" ] ] ] #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" => "1340978" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1340976" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1225 #items: array:2 [ 0 => App\Models\Task {#1233 #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" => 1319408 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "16" "field_page_end" => null "field_url" => "/10-klass/fizika/gelfgat-zadachnik/02-1" "field_display_title" => "2.1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1234 #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 {#1235 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1236 #items: array:1 [ 0 => App\Models\Branch {#1126} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1237 #items: array:4 [ 0 => App\Models\Branch {#1126} 1 => App\Models\Branch {#1130} 2 => App\Models\Branch {#1134} 3 => App\Models\Branch {#1138} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1239 #items: array:2 [ 0 => App\Models\Element {#1248 #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" => 1493689 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1249 #items: array:1 [ 0 => App\Models\Edition {#1106} ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1319408" "type" => "task" ] "text" => "<p><strong>2.1.</strong> От движущегося поезда отцепляют последний вагон, после чего поезд продолжает двигаться с неизменной скоростью, а скорость вагона уменьшается. Путь, пройденный вагоном от момента отцепления до остановки, равен 50 м. Какой путь прошел за это время поезд, если считать, что вагон двигался с постоянным ускорением?</p><p>☑ 100 м.</p><p><strong><em>Решение.</em></strong> Пусть скорость поезда $v_0$, время движения вагона $\text{t}$. Тогда поезд до остановки вагона пройдет путь $s_\text{п} = v_0t$. Средняя скорость движения вагона за это время $v_\text{ср} = v_0/2$, поэтому пройденный вагоном путь вдвое меньше.</p><p>Этот результат становится очевидным, если построить график зависимости скорости от времени для поезда и вагона (см. рисунок) и учесть, что перемещение численно равно площади под графиком $v(t)$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "1-1.jpg" "alt" => null "width" => "1432" "height" => 1081 "path" => "/media/fizika_10/gelfgat-z/0-02/1-1.webp?ts=1756251003" ] ] ] #original: array:7 [ "id" => 1493689 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1249} "task" => array:2 [ "refs" => "1319408" "type" => "task" ] "text" => "<p><strong>2.1.</strong> От движущегося поезда отцепляют последний вагон, после чего поезд продолжает двигаться с неизменной скоростью, а скорость вагона уменьшается. Путь, пройденный вагоном от момента отцепления до остановки, равен 50 м. Какой путь прошел за это время поезд, если считать, что вагон двигался с постоянным ускорением?</p><p>☑ 100 м.</p><p><strong><em>Решение.</em></strong> Пусть скорость поезда $v_0$, время движения вагона $\text{t}$. Тогда поезд до остановки вагона пройдет путь $s_\text{п} = v_0t$. Средняя скорость движения вагона за это время $v_\text{ср} = v_0/2$, поэтому пройденный вагоном путь вдвое меньше.</p><p>Этот результат становится очевидным, если построить график зависимости скорости от времени для поезда и вагона (см. рисунок) и учесть, что перемещение численно равно площади под графиком $v(t)$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "1-1.jpg" "alt" => null "width" => "1432" "height" => 1081 "path" => "/media/fizika_10/gelfgat-z/0-02/1-1.webp?ts=1756251003" ] ] ] #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 {#1250 #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" => 1691246 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1251 #items: array:1 [ 0 => App\Models\Edition {#1100} ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1319408" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Путь, пройденный вагоном до остановки, $S_в = 50$ м.</p><p>Движение поезда – равномерное, со скоростью $v_п = v_0 = const$.</p><p>Движение вагона – равноускоренное (равнозамедленное), с ускорением $a_в = const$.</p><p>Начальная скорость вагона равна скорости поезда, $v_{0в} = v_0$.</p><p>Конечная скорость вагона, $v_к = 0$.</p><p><strong>Найти:</strong></p><p>Путь, пройденный поездом за время остановки вагона, $S_п$ - ?</p><p><strong>Решение:</strong></p><p>Пусть $t$ – время, которое прошло с момента отцепления вагона до его полной остановки. В начальный момент времени (момент отцепления) и поезд, и вагон имели одинаковую скорость, обозначим ее $v_0$.</p><p>Поезд продолжает двигаться с постоянной скоростью $v_0$. Путь, пройденный поездом за время $t$, определяется по формуле для равномерного движения:</p><p>$S_п = v_0 \cdot t$</p><p>Вагон движется равнозамедленно с начальной скоростью $v_0$ и конечной скоростью $v_к = 0$. Путь, пройденный вагоном, можно найти через среднюю скорость движения.</p><p>Средняя скорость вагона при равноускоренном движении равна полусумме начальной и конечной скоростей:</p><p>$v_{ср} = \frac{v_0 + v_к}{2}$</p><p>Поскольку вагон останавливается, $v_к = 0$, то его средняя скорость равна:</p><p>$v_{ср} = \frac{v_0 + 0}{2} = \frac{v_0}{2}$</p><p>Путь, пройденный вагоном, равен произведению его средней скорости на время движения:</p><p>$S_в = v_{ср} \cdot t = \frac{v_0}{2} \cdot t$</p><p>Мы получили систему из двух уравнений:</p><p>$S_п = v_0 t$</p><p>$S_в = \frac{v_0 t}{2}$</p><p>Из второго уравнения видно, что путь, пройденный поездом ($v_0 t$), в два раза больше пути, пройденного вагоном.</p><p>$v_0 t = 2 \cdot S_в$</p><p>Следовательно:</p><p>$S_п = 2 \cdot S_в$</p><p>Подставим известное значение $S_в = 50$ м:</p><p>$S_п = 2 \cdot 50 = 100$ м.</p><p><strong>Ответ:</strong> 100 м.</p>" ] #original: array:6 [ "id" => 1691246 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1251} "task" => array:2 [ "refs" => "1319408" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Путь, пройденный вагоном до остановки, $S_в = 50$ м.</p><p>Движение поезда – равномерное, со скоростью $v_п = v_0 = const$.</p><p>Движение вагона – равноускоренное (равнозамедленное), с ускорением $a_в = const$.</p><p>Начальная скорость вагона равна скорости поезда, $v_{0в} = v_0$.</p><p>Конечная скорость вагона, $v_к = 0$.</p><p><strong>Найти:</strong></p><p>Путь, пройденный поездом за время остановки вагона, $S_п$ - ?</p><p><strong>Решение:</strong></p><p>Пусть $t$ – время, которое прошло с момента отцепления вагона до его полной остановки. В начальный момент времени (момент отцепления) и поезд, и вагон имели одинаковую скорость, обозначим ее $v_0$.</p><p>Поезд продолжает двигаться с постоянной скоростью $v_0$. Путь, пройденный поездом за время $t$, определяется по формуле для равномерного движения:</p><p>$S_п = v_0 \cdot t$</p><p>Вагон движется равнозамедленно с начальной скоростью $v_0$ и конечной скоростью $v_к = 0$. Путь, пройденный вагоном, можно найти через среднюю скорость движения.</p><p>Средняя скорость вагона при равноускоренном движении равна полусумме начальной и конечной скоростей:</p><p>$v_{ср} = \frac{v_0 + v_к}{2}$</p><p>Поскольку вагон останавливается, $v_к = 0$, то его средняя скорость равна:</p><p>$v_{ср} = \frac{v_0 + 0}{2} = \frac{v_0}{2}$</p><p>Путь, пройденный вагоном, равен произведению его средней скорости на время движения:</p><p>$S_в = v_{ср} \cdot t = \frac{v_0}{2} \cdot t$</p><p>Мы получили систему из двух уравнений:</p><p>$S_п = v_0 t$</p><p>$S_в = \frac{v_0 t}{2}$</p><p>Из второго уравнения видно, что путь, пройденный поездом ($v_0 t$), в два раза больше пути, пройденного вагоном.</p><p>$v_0 t = 2 \cdot S_в$</p><p>Следовательно:</p><p>$S_п = 2 \cdot S_в$</p><p>Подставим известное значение $S_в = 50$ м:</p><p>$S_п = 2 \cdot 50 = 100$ м.</p><p><strong>Ответ:</strong> 100 м.</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" => "1319409" "type" => "task" ] "previous" => array:2 [ "refs" => "1319407" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1245 #items: array:1 [ 0 => App\Models\Book {#1056} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1340977" "type" => "book_page" ] ] #original: array:24 [ "id" => 1319408 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "16" "field_page_end" => null "field_url" => "/10-klass/fizika/gelfgat-zadachnik/02-1" "field_display_title" => "2.1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1234} "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 {#1235} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1236} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1237} "content" => Illuminate\Database\Eloquent\Collection {#1239} "next" => array:2 [ "refs" => "1319409" "type" => "task" ] "previous" => array:2 [ "refs" => "1319407" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1245} "page" => array:2 [ "refs" => "1340977" "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 {#1240 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" 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№2.2 (с. 16)
Условие. №2.2 (с. 16)
скриншот условия
2.2. От толчка шарик вкатывается на наклонную плоскость. На расстоянии $l = 30$ см от начала движения шарик побывал дважды: через $t_1 = 1$ с и $t_2 = 2$ с после толчка. Считая движение равноускоренным, найдите начальную скорость $v_0$ и ускорение $\text{a}$.
☑ $45 \frac{см} {с}$ $30 \frac{см} {с^2}$.
Решение. Зависимость координаты шарика от времени выражается формулой $x = v_{0x}t - \frac{a_x t^2}{2}$. Отсюда получаем квадратное уравнение $t^2 - \frac{2v_{0x}}{a_x}t + \frac{2x}{a_x} = 0$. Так как $t_1$ и $t_2$ — корни этого уравнения при $x = l$, то согласно теореме Виета $t_1 + t_2 = \frac{2v_{0x}}{a_x}$ и $t_1 t_2 = \frac{2l}{a_x}$. Из полученной системы уравнений находим: $a_x = \frac{2l}{t_1 t_2} = 30 \text{ (см/с}^2\text{)}$, $v_{0x} = \frac{(t_1 + t_2) \cdot a_x}{2} = 45 \text{ (см/с)}$.
Решение. №2.2 (с. 16)
Дано:
$l = 30 \text{ см}$
$t_1 = 1 \text{ с}$
$t_2 = 2 \text{ с}$
Перевод в систему СИ:
$l = 30 \text{ см} = 0.3 \text{ м}$
Найти:
$v_0$ - начальная скорость
$a$ - ускорение
Решение:
Движение шарика по наклонной плоскости является равноускоренным. Зависимость координаты шарика $x$ от времени $t$ описывается уравнением:
$x(t) = v_0 t + \frac{at^2}{2}$
где $v_0$ — начальная скорость, а $a$ — ускорение. Поскольку шарик вкатывается на наклонную плоскость, его скорость уменьшается, следовательно, вектор ускорения направлен против вектора начальной скорости, и проекция ускорения на ось движения будет отрицательной.
По условию задачи, в моменты времени $t_1$ и $t_2$ шарик находится на одном и том же расстоянии $l$ от начала движения. Это означает, что $t_1$ и $t_2$ являются корнями уравнения $l = v_0 t + \frac{at^2}{2}$ относительно времени $t$.
Перепишем это уравнение в виде стандартного квадратного уравнения относительно $t$ ($At^2 + Bt + C = 0$):
$\frac{a}{2}t^2 + v_0 t - l = 0$
Согласно теореме Виета, для квадратного уравнения сумма корней равна $-B/A$, а произведение корней равно $C/A$.
В нашем случае коэффициенты равны: $A = \frac{a}{2}$, $B = v_0$, $C = -l$.
Применим теорему Виета к нашему уравнению:
Сумма корней: $t_1 + t_2 = -\frac{v_0}{a/2} = -\frac{2v_0}{a}$
Произведение корней: $t_1 t_2 = \frac{-l}{a/2} = -\frac{2l}{a}$
Мы получили систему из двух уравнений с двумя неизвестными $v_0$ и $a$:
$\begin{cases} t_1 + t_2 = -2v_0/a \\ t_1 t_2 = -2l/a \end{cases}$
Из второго уравнения выразим ускорение $a$:
$a = -\frac{2l}{t_1 t_2}$
Из первого уравнения выразим начальную скорость $v_0$:
$v_0 = -\frac{a(t_1 + t_2)}{2}$
Подставим известные значения (для удобства будем производить вычисления в исходных единицах, см и с):
$l = 30 \text{ см}$, $t_1 = 1 \text{ с}$, $t_2 = 2 \text{ с}$.
Найдем ускорение:
$a = -\frac{2 \cdot 30 \text{ см}}{1 \text{ с} \cdot 2 \text{ с}} = -\frac{60 \text{ см}}{2 \text{ с}^2} = -30 \text{ см/с}^2$
Теперь найдем начальную скорость:
$v_0 = -\frac{(-30 \text{ см/с}^2) \cdot (1 \text{ с} + 2 \text{ с})}{2} = -\frac{(-30 \text{ см/с}^2) \cdot 3 \text{ с}}{2} = \frac{90 \text{ см/с}}{2} = 45 \text{ см/с}$
Таким образом, начальная скорость шарика равна 45 см/с, а его ускорение равно -30 см/с². Отрицательный знак ускорения подтверждает, что движение является равнозамедленным.
Ответ: начальная скорость $v_0 = 45 \text{ см/с}$; ускорение $a = -30 \text{ см/с}^2$ (модуль ускорения равен $30 \text{ см/с}^2$).
Другие задания:
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