Вариант 1, страница 62 - гдз по физике 9 класс дидактические материалы Марон, Марон

Физика, 9 класс Дидактические материалы, авторы: Марон Абрам Евсеевич, Марон Евгений Абрамович, издательство Просвещение, Москва, 2022, белого цвета

Авторы: Марон А. Е., Марон Е. А.

Тип: Дидактические материалы

Издательство: Просвещение

Год издания: 2022 - 2026

Уровень обучения: базовый

Цвет обложки: белый изображена башня

ISBN: 978-5-09-111414-0

Самостоятельные работы. СР-4. Прямолинейное равноускоренное движение - страница 62.

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              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1106
              #items: []
              #escapeWhenCastingToString: false
            }
          ]
          #original: array:24 [
            "id" => 1428174
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Самостоятельные работы"
            "field_branch_order" => null
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1074}
            "field_page_start" => "53"
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            "field_display_branch_in_title" => "1"
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            "field_h1" => null
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            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1072}
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1106}
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          #attributeCastCache: []
          #dateFormat: null
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          #touches: []
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          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
        1 => App\Models\Branch {#1107
          #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" => 1428178
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
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            "field_branch_order" => null
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1108
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              #escapeWhenCastingToString: false
            }
            "field_page_start" => "62"
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            "book" => Illuminate\Database\Eloquent\Collection {#1109
              #items: array:1 [
                0 => App\Models\Book {#1110
                  #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" => 894
                    "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 {#1111
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                      #escapeWhenCastingToString: false
                    }
                    "field_class" => Illuminate\Database\Eloquent\Collection {#1113
                      #items: array:1 [ …1]
                      #escapeWhenCastingToString: false
                    }
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1115
                      #items: array:1 [ …1]
                      #escapeWhenCastingToString: false
                    }
                    "field_author" => Illuminate\Database\Eloquent\Collection {#1117
                      #items: array:2 [ …2]
                      #escapeWhenCastingToString: false
                    }
                    "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1120
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_book_type" => Illuminate\Database\Eloquent\Collection {#1121
                      #items: array:1 [ …1]
                      #escapeWhenCastingToString: false
                    }
                    "field_country" => Illuminate\Database\Eloquent\Collection {#1123
                      #items: array:1 [ …1]
                      #escapeWhenCastingToString: false
                    }
                    "field_city" => Illuminate\Database\Eloquent\Collection {#1125
                      #items: array:1 [ …1]
                      #escapeWhenCastingToString: false
                    }
                    "field_series" => Illuminate\Database\Eloquent\Collection {#1127
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_umk" => Illuminate\Database\Eloquent\Collection {#1128
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1129
                      #items: array:1 [ …1]
                      #escapeWhenCastingToString: false
                    }
                    "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1131
                      #items: array:1 [ …1]
                      #escapeWhenCastingToString: false
                    }
                    "field_publication_number" => "3"
                    "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1133
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                      #escapeWhenCastingToString: false
                    }
                    "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1135
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_under_the_edition_degree" => null
                    "field_cover_description" => "изображена башня"
                    "field_publication_year" => "2022"
                    "field_publication_year_until" => null
                    "field_part" => ""
                    "field_part_writing" => ""
                    "field_second_foreign_language" => null
                    "field_for_whom" => "Учебное пособие"
                    "field_allowed" => null
                    "field_reserve_field" => null
                    "field_link_to_source" => null
                    "field_tasks_count" => "674"
                    "field_priority" => null
                    "field_default_folder" => "/fizika_09/maron-dm/"
                    "field_isbn" => "978-5-09-111414-0"
                    "field_cover" => array:1 [
                      0 => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880"
                    ]
                    "field_cover_alts" => array:1 [
                      0 => ""
                    ]
                    "field_covers" => array:1 [
                      0 => array:4 [ …4]
                    ]
                    "field_popular_book" => "0"
                    "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1136
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                      #escapeWhenCastingToString: false
                    }
                    "field_new_book" => Illuminate\Database\Eloquent\Collection {#1137
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                      #escapeWhenCastingToString: false
                    }
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                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy"
                    "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1139
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                      #escapeWhenCastingToString: false
                    }
                    "field_metatags_title" => null
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                    ]
                  ]
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                    "field_subject" => Illuminate\Database\Eloquent\Collection {#1111}
                    "field_class" => Illuminate\Database\Eloquent\Collection {#1113}
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1115}
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                    "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1120}
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                    "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1129}
                    "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1131}
                    "field_publication_number" => "3"
                    "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1133}
                    "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1135}
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                    "field_cover_description" => "изображена башня"
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                    "field_part" => ""
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                    "field_allowed" => null
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                    "field_link_to_source" => null
                    "field_tasks_count" => "674"
                    "field_priority" => null
                    "field_default_folder" => "/fizika_09/maron-dm/"
                    "field_isbn" => "978-5-09-111414-0"
                    "field_cover" => array:1 [
                      0 => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880"
                    ]
                    "field_cover_alts" => array:1 [
                      0 => ""
                    ]
                    "field_covers" => array:1 [
                      0 => array:4 [ …4]
                    ]
                    "field_popular_book" => "0"
                    "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1136}
                    "field_new_book" => Illuminate\Database\Eloquent\Collection {#1137}
                    "field_old_book" => Illuminate\Database\Eloquent\Collection {#1138}
                    "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy"
                    "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1139}
                    "field_metatags_title" => null
                    "field_metatags_description" => null
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                    "field_description_bottom" => null
                    "breadcrumbs" => array:3 [
                      "class" => 380
                      "subject" => 556
                      "class_subject" => 493
                    ]
                  ]
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                  #touches: []
                  +timestamps: true
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                  #visible: []
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                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1141
              #items: array:1 [
                0 => App\Models\Branch {#1142
                  #connection: "mysql"
                  #table: "branches"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
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                  +exists: true
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                  #attributes: array:24 [
                    "id" => 1428174
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
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                    "field_url" => null
                    "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1143
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_page_start" => "53"
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                    "field_branch_title_in_content" => "0"
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                    "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 {#1144
                      #items: array:1 [ …1]
                      #escapeWhenCastingToString: false
                    }
                    "branch_parent" => Illuminate\Database\Eloquent\Collection {#1145
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                  ]
                  #original: array:24 [
                    "id" => 1428174
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_display_title" => "Самостоятельные работы"
                    "field_branch_order" => null
                    "field_url" => null
                    "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1143}
                    "field_page_start" => "53"
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                    "field_display_task_interval" => "0"
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                    "branch_parent" => Illuminate\Database\Eloquent\Collection {#1145}
                  ]
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                  #touches: []
                  +timestamps: true
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                  #hidden: []
                  #visible: []
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                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
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          ]
          #original: array:24 [
            "id" => 1428178
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "СР-4. Прямолинейное равноускоренное движение"
            "field_branch_order" => null
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1108}
            "field_page_start" => "62"
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            "field_display_branch_in_title" => "1"
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            "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 {#1109}
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1141}
          ]
          #changes: []
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            0 => "*"
          ]
        }
      ]
      #escapeWhenCastingToString: false
    }
    "content" => Illuminate\Database\Eloquent\Collection {#1163
      #items: array:2 [
        0 => App\Models\Element {#1148
          #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" => 1682915
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1149
              #items: array:1 [
                0 => App\Models\Edition {#1147
                  #connection: "mysql"
                  #table: "editions"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
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                  #escapeWhenCastingToString: false
                  #attributes: array:21 [
                    "id" => 5992
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "title" => "Условие"
                    "field_order" => "1"
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1150
                      #items: array:1 [ …1]
                      #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 {#1152
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_comment" => null
                    "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1153
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_process_formula" => "katex"
                    "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1154
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                      #escapeWhenCastingToString: false
                    }
                    "field_content_source" => null
                  ]
                  #original: array:21 [
                    "id" => 5992
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "title" => "Условие"
                    "field_order" => "1"
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                    "field_solution_author" => "Автор"
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                    "field_comment" => null
                    "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1153}
                    "field_process_formula" => "katex"
                    "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1154}
                    "field_content_source" => null
                  ]
                  #changes: []
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                  #dateFormat: null
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                  #touches: []
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                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "task" => array:2 [
              "refs" => "1428600"
              "type" => "task"
            ]
            "text" => "<p><strong>1.</strong> При подходе к станции поезд, имея начальную скорость 90 км/ч, остановился за 50 с. Определите его ускорение при торможении.</p><p><strong>2.</strong> Автомобиль за 10 с увеличил скорость с 18 до 27 км/ч. Определите ускорение и путь, пройденный автомобилем за это время.</p>"
            "img" => array:1 [
              0 => array:5 [
                "name" => "1-1.jpg"
                "alt" => null
                "width" => "1400"
                "height" => 423
                "path" => "/media/fizika_09/maron-dm/0-cp04/1-1.webp?ts=1758964220"
              ]
            ]
          ]
          #original: array:7 [
            "id" => 1682915
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1149}
            "task" => array:2 [
              "refs" => "1428600"
              "type" => "task"
            ]
            "text" => "<p><strong>1.</strong> При подходе к станции поезд, имея начальную скорость 90 км/ч, остановился за 50 с. Определите его ускорение при торможении.</p><p><strong>2.</strong> Автомобиль за 10 с увеличил скорость с 18 до 27 км/ч. Определите ускорение и путь, пройденный автомобилем за это время.</p>"
            "img" => array:1 [
              0 => array:5 [
                "name" => "1-1.jpg"
                "alt" => null
                "width" => "1400"
                "height" => 423
                "path" => "/media/fizika_09/maron-dm/0-cp04/1-1.webp?ts=1758964220"
              ]
            ]
          ]
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          #attributeCastCache: []
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          #touches: []
          +timestamps: true
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          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
        1 => App\Models\Element {#1155
          #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" => 1730617
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1156
              #items: array:1 [
                0 => App\Models\Edition {#1157
                  #connection: "mysql"
                  #table: "editions"
                  #primaryKey: "id"
                  #keyType: "int"
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            "text" => "<p><strong>1.</strong> <strong>Дано:</strong></p><p>Начальная скорость, $v_0 = 90$ км/ч<br>Конечная скорость, $v = 0$ м/с (поезд остановился)<br>Время торможения, $t = 50$ с</p><p>Переведем начальную скорость в систему СИ (м/с):<br>$v_0 = 90 \frac{км}{ч} = \frac{90 \cdot 1000 \text{ м}}{3600 \text{ с}} = 25 \text{ м/с}$</p><p><strong>Найти:</strong></p><p>Ускорение, $a - ?$</p><p><strong>Решение:</strong></p><p>Движение поезда при торможении является равнозамедленным. Ускорение для такого движения можно найти по формуле:<br>$a = \frac{v - v_0}{t}$<br>Подставим известные значения в эту формулу:<br>$a = \frac{0 \text{ м/с} - 25 \text{ м/с}}{50 \text{ с}} = -\frac{25}{50} \frac{м}{с^2} = -0.5 \frac{м}{с^2}$<br>Знак "минус" указывает, что вектор ускорения направлен противоположно вектору начальной скорости, что соответствует процессу торможения.</p><p><strong>Ответ:</strong> ускорение поезда при торможении равно $-0.5$ м/с².</p><p><strong>2.</strong> <strong>Дано:</strong></p><p>Время, $t = 10$ с<br>Начальная скорость, $v_0 = 18$ км/ч<br>Конечная скорость, $v = 27$ км/ч</p><p>Переведем значения скоростей в систему СИ (м/с):<br>$v_0 = 18 \frac{км}{ч} = \frac{18 \cdot 1000 \text{ м}}{3600 \text{ с}} = 5 \text{ м/с}$<br>$v = 27 \frac{км}{ч} = \frac{27 \cdot 1000 \text{ м}}{3600 \text{ с}} = 7.5 \text{ м/с}$</p><p><strong>Найти:</strong></p><p>Ускорение, $a - ?$<br>Путь, $s - ?$</p><p><strong>Решение:</strong></p><p>Так как скорость изменяется равномерно, движение автомобиля является равноускоренным. Сначала определим ускорение по формуле:<br>$a = \frac{v - v_0}{t}$<br>Подставим числовые значения:<br>$a = \frac{7.5 \text{ м/с} - 5 \text{ м/с}}{10 \text{ с}} = \frac{2.5}{10} \frac{м}{с^2} = 0.25 \frac{м}{с^2}$<br>Далее найдем путь, пройденный автомобилем за это время. Для этого можно использовать формулу пути при равноускоренном движении:<br>$s = v_0 t + \frac{at^2}{2}$<br>Или более простую в данном случае формулу, использующую среднюю скорость:<br>$s = \frac{v + v_0}{2} \cdot t$<br>Подставим известные значения во вторую формулу:<br>$s = \frac{7.5 \text{ м/с} + 5 \text{ м/с}}{2} \cdot 10 \text{ с} = \frac{12.5}{2} \cdot 10 \text{ м} = 6.25 \cdot 10 \text{ м} = 62.5 \text{ м}$</p><p><strong>Ответ:</strong> ускорение автомобиля равно $0.25$ м/с², а пройденный путь составляет $62.5$ м.</p>"
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            "text" => "<p><strong>1.</strong> <strong>Дано:</strong></p><p>Начальная скорость, $v_0 = 90$ км/ч<br>Конечная скорость, $v = 0$ м/с (поезд остановился)<br>Время торможения, $t = 50$ с</p><p>Переведем начальную скорость в систему СИ (м/с):<br>$v_0 = 90 \frac{км}{ч} = \frac{90 \cdot 1000 \text{ м}}{3600 \text{ с}} = 25 \text{ м/с}$</p><p><strong>Найти:</strong></p><p>Ускорение, $a - ?$</p><p><strong>Решение:</strong></p><p>Движение поезда при торможении является равнозамедленным. Ускорение для такого движения можно найти по формуле:<br>$a = \frac{v - v_0}{t}$<br>Подставим известные значения в эту формулу:<br>$a = \frac{0 \text{ м/с} - 25 \text{ м/с}}{50 \text{ с}} = -\frac{25}{50} \frac{м}{с^2} = -0.5 \frac{м}{с^2}$<br>Знак "минус" указывает, что вектор ускорения направлен противоположно вектору начальной скорости, что соответствует процессу торможения.</p><p><strong>Ответ:</strong> ускорение поезда при торможении равно $-0.5$ м/с².</p><p><strong>2.</strong> <strong>Дано:</strong></p><p>Время, $t = 10$ с<br>Начальная скорость, $v_0 = 18$ км/ч<br>Конечная скорость, $v = 27$ км/ч</p><p>Переведем значения скоростей в систему СИ (м/с):<br>$v_0 = 18 \frac{км}{ч} = \frac{18 \cdot 1000 \text{ м}}{3600 \text{ с}} = 5 \text{ м/с}$<br>$v = 27 \frac{км}{ч} = \frac{27 \cdot 1000 \text{ м}}{3600 \text{ с}} = 7.5 \text{ м/с}$</p><p><strong>Найти:</strong></p><p>Ускорение, $a - ?$<br>Путь, $s - ?$</p><p><strong>Решение:</strong></p><p>Так как скорость изменяется равномерно, движение автомобиля является равноускоренным. Сначала определим ускорение по формуле:<br>$a = \frac{v - v_0}{t}$<br>Подставим числовые значения:<br>$a = \frac{7.5 \text{ м/с} - 5 \text{ м/с}}{10 \text{ с}} = \frac{2.5}{10} \frac{м}{с^2} = 0.25 \frac{м}{с^2}$<br>Далее найдем путь, пройденный автомобилем за это время. Для этого можно использовать формулу пути при равноускоренном движении:<br>$s = v_0 t + \frac{at^2}{2}$<br>Или более простую в данном случае формулу, использующую среднюю скорость:<br>$s = \frac{v + v_0}{2} \cdot t$<br>Подставим известные значения во вторую формулу:<br>$s = \frac{7.5 \text{ м/с} + 5 \text{ м/с}}{2} \cdot 10 \text{ с} = \frac{12.5}{2} \cdot 10 \text{ м} = 6.25 \cdot 10 \text{ м} = 62.5 \text{ м}$</p><p><strong>Ответ:</strong> ускорение автомобиля равно $0.25$ м/с², а пройденный путь составляет $62.5$ м.</p>"
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                      "field_creative_case" => "дидактическими материалами"
                      "field_dative_case" => "дидактическим материалам"
                      "field_genitive_case" => "дидактических материалов"
                      "field_nominative_case" => "дидактические материалы"
                      "field_prepositional_case" => "дидактических материалах"
                    ]
                    "field_plural_form" => null
                    "field_short_name" => null
                    "field_short_name_foreign" => null
                    "field_translit" => "didakticheskie materialy"
                  ]
                  #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 {#1177
              #items: array:1 [
                0 => App\Models\Term {#1178
                  #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
                       …4
                    ]
                    "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 {#1179
              #items: array:1 [
                0 => App\Models\Term {#1180
                  #connection: "mysql"
                  #table: "terms"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:6 [
                    "id" => 15
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Москва"
                    "field_cases" => array:6 [ …6]
                    "field_translit" => "moskva"
                  ]
                  #original: array:6 [
                    "id" => 15
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Москва"
                    "field_cases" => array:6 [ …6]
                    "field_translit" => "moskva"
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "field_series" => Illuminate\Database\Eloquent\Collection {#1181
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_umk" => Illuminate\Database\Eloquent\Collection {#1182
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1183
              #items: array:1 [
                0 => App\Models\Term {#1184
                  #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" => 38
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "базовый"
                    "field_cases" => array:6 [ …6]
                    "field_translit" => "bazovyy"
                  ]
                  #original: array:6 [
                    "id" => 38
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "базовый"
                    "field_cases" => array:6 [ …6]
                    "field_translit" => "bazovyy"
                  ]
                  #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 {#1185
              #items: array:1 [
                0 => App\Models\Term {#1186
                  #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" => 25
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "ФГОС (новый)"
                    "field_cases" => array:6 [ …6]
                    "field_color" => "красный"
                    "field_end_year" => "2027"
                    "field_start_year" => "2023"
                    "field_translit" => "fgos"
                    "field_type" => "новый"
                  ]
                  #original: array:10 [
                    "id" => 25
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "ФГОС (новый)"
                    "field_cases" => array:6 [ …6]
                    "field_color" => "красный"
                    "field_end_year" => "2027"
                    "field_start_year" => "2023"
                    "field_translit" => "fgos"
                    "field_type" => "новый"
                  ]
                  #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_publication_number" => "3"
            "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1187
              #items: array:1 [
                0 => App\Models\Term {#1188
                  #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" => 34
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "переработанное"
                    "field_cases" => array:6 [ …6]
                    "field_translit" => "pererabotannoe"
                  ]
                  #original: array:6 [
                    "id" => 34
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "переработанное"
                    "field_cases" => array:6 [ …6]
                    "field_translit" => "pererabotannoe"
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
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                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1189
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_under_the_edition_degree" => null
            "field_cover_description" => "изображена башня"
            "field_publication_year" => "2022"
            "field_publication_year_until" => null
            "field_part" => ""
            "field_part_writing" => ""
            "field_second_foreign_language" => null
            "field_for_whom" => "Учебное пособие"
            "field_allowed" => null
            "field_reserve_field" => null
            "field_link_to_source" => null
            "field_tasks_count" => "674"
            "field_priority" => null
            "field_default_folder" => "/fizika_09/maron-dm/"
            "field_isbn" => "978-5-09-111414-0"
            "field_cover" => array:1 [
              0 => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880"
            ]
            "field_cover_alts" => array:1 [
              0 => ""
            ]
            "field_covers" => array:1 [
              0 => array:4 [
                "path" => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880"
                "alt" => ""
                "width" => "1888"
                "height" => "2427"
              ]
            ]
            "field_popular_book" => "0"
            "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1190
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_new_book" => Illuminate\Database\Eloquent\Collection {#1191
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_old_book" => Illuminate\Database\Eloquent\Collection {#1192
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy"
            "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1193
              #items: array:1 [
                0 => App\Models\Term {#1194
                  #connection: "mysql"
                  #table: "terms"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:6 [
                    "id" => 45
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "белый"
                    "field_cases" => array:6 [ …6]
                    "field_translit" => "belyy"
                  ]
                  #original: array:6 [
                    "id" => 45
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "белый"
                    "field_cases" => array:6 [ …6]
                    "field_translit" => "belyy"
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
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                  #touches: []
                  +timestamps: true
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                  #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" => 894
            "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 {#1166}
            "field_class" => Illuminate\Database\Eloquent\Collection {#1167}
            "field_publisher" => Illuminate\Database\Eloquent\Collection {#1169}
            "field_author" => Illuminate\Database\Eloquent\Collection {#1171}
            "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1174}
            "field_book_type" => Illuminate\Database\Eloquent\Collection {#1175}
            "field_country" => Illuminate\Database\Eloquent\Collection {#1177}
            "field_city" => Illuminate\Database\Eloquent\Collection {#1179}
            "field_series" => Illuminate\Database\Eloquent\Collection {#1181}
            "field_umk" => Illuminate\Database\Eloquent\Collection {#1182}
            "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1183}
            "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1185}
            "field_publication_number" => "3"
            "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1187}
            "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1189}
            "field_under_the_edition_degree" => null
            "field_cover_description" => "изображена башня"
            "field_publication_year" => "2022"
            "field_publication_year_until" => null
            "field_part" => ""
            "field_part_writing" => ""
            "field_second_foreign_language" => null
            "field_for_whom" => "Учебное пособие"
            "field_allowed" => null
            "field_reserve_field" => null
            "field_link_to_source" => null
            "field_tasks_count" => "674"
            "field_priority" => null
            "field_default_folder" => "/fizika_09/maron-dm/"
            "field_isbn" => "978-5-09-111414-0"
            "field_cover" => array:1 [
              0 => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880"
            ]
            "field_cover_alts" => array:1 [
              0 => ""
            ]
            "field_covers" => array:1 [
              0 => array:4 [
                "path" => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880"
                "alt" => ""
                "width" => "1888"
                "height" => "2427"
              ]
            ]
            "field_popular_book" => "0"
            "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1190}
            "field_new_book" => Illuminate\Database\Eloquent\Collection {#1191}
            "field_old_book" => Illuminate\Database\Eloquent\Collection {#1192}
            "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy"
            "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1193}
            "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: []
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          #classCastCache: []
          #attributeCastCache: []
          #dateFormat: null
          #appends: []
          #dispatchesEvents: []
          #observables: []
          #relations: []
          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
      ]
      #escapeWhenCastingToString: false
    }
    "page" => Illuminate\Database\Eloquent\Collection {#1211
      #items: array:1 [
        0 => App\Models\BookPage {#1210
          #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" => 1428953
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_page_start" => "62"
            "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/page-62"
            "field_display_title" => "62"
            "field_folder" => "1"
            "field_image_name" => "62"
            "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1212
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_weight" => "0"
            "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1213
              #items: array:1 [
                0 => App\Models\Book {#1165}
              ]
              #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 {#1214
              #items: []
              #escapeWhenCastingToString: false
            }
            "content" => Illuminate\Database\Eloquent\Collection {#1225
              #items: array:1 [
                0 => App\Models\Element {#1215
                  #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" => 1683620
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "edition" => Illuminate\Database\Eloquent\Collection {#1217 …2}
                    "book_page" => array:2 [ …2]
                    "img" => array:1 [ …1]
                  ]
                  #original: array:6 [
                    "id" => 1683620
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "edition" => Illuminate\Database\Eloquent\Collection {#1217 …2}
                    "book_page" => array:2 [ …2]
                    "img" => array:1 [ …1]
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "next" => array:2 [
              "refs" => "1428954"
              "type" => "book_page"
            ]
            "previous" => array:2 [
              "refs" => "1428952"
              "type" => "book_page"
            ]
            "tasks" => Illuminate\Database\Eloquent\Collection {#1521
              #items: array:4 [
                0 => App\Models\Task {#1531
                  #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" => 1428599
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_page_start" => "62"
                    "field_page_end" => null
                    "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp03-10"
                    "field_display_title" => "Вариант 10"
                    "field_outside_task" => null
                    "field_task_type" => Illuminate\Database\Eloquent\Collection {#1532 …2}
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "field_match" => null
                    "breadcrumbs" => []
                    "edition_groups" => Illuminate\Database\Eloquent\Collection {#1533 …2}
                    "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1534 …2}
                    "parent_branches" => Illuminate\Database\Eloquent\Collection {#1572 …2}
                    "content" => Illuminate\Database\Eloquent\Collection {#1558 …2}
                    "next" => array:2 [ …2]
                    "previous" => array:2 [ …2]
                    "book" => Illuminate\Database\Eloquent\Collection {#1555 …2}
                    "page" => array:2 [ …2]
                  ]
                  #original: array:24 [
                    "id" => 1428599
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_page_start" => "62"
                    "field_page_end" => null
                    "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp03-10"
                    "field_display_title" => "Вариант 10"
                    "field_outside_task" => null
                    "field_task_type" => Illuminate\Database\Eloquent\Collection {#1532 …2}
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "field_match" => null
                    "breadcrumbs" => []
                    "edition_groups" => Illuminate\Database\Eloquent\Collection {#1533 …2}
                    "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1534 …2}
                    "parent_branches" => Illuminate\Database\Eloquent\Collection {#1572 …2}
                    "content" => Illuminate\Database\Eloquent\Collection {#1558 …2}
                    "next" => array:2 [ …2]
                    "previous" => array:2 [ …2]
                    "book" => Illuminate\Database\Eloquent\Collection {#1555 …2}
                    "page" => array:2 [ …2]
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
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Вариант 1 (с. 62)
Условие. Вариант 1 (с. 62)
скриншот условия
Физика, 9 класс Дидактические материалы, авторы: Марон Абрам Евсеевич, Марон Евгений Абрамович, издательство Просвещение, Москва, 2022, белого цвета, страница 62, Условие

1. При подходе к станции поезд, имея начальную скорость 90 км/ч, остановился за 50 с. Определите его ускорение при торможении.

2. Автомобиль за 10 с увеличил скорость с 18 до 27 км/ч. Определите ускорение и путь, пройденный автомобилем за это время.

Решение. Вариант 1 (с. 62)

1. Дано:

Начальная скорость, $v_0 = 90$ км/ч
Конечная скорость, $v = 0$ м/с (поезд остановился)
Время торможения, $t = 50$ с

Переведем начальную скорость в систему СИ (м/с):
$v_0 = 90 \frac{км}{ч} = \frac{90 \cdot 1000 \text{ м}}{3600 \text{ с}} = 25 \text{ м/с}$

Найти:

Ускорение, $a - ?$

Решение:

Движение поезда при торможении является равнозамедленным. Ускорение для такого движения можно найти по формуле:
$a = \frac{v - v_0}{t}$
Подставим известные значения в эту формулу:
$a = \frac{0 \text{ м/с} - 25 \text{ м/с}}{50 \text{ с}} = -\frac{25}{50} \frac{м}{с^2} = -0.5 \frac{м}{с^2}$
Знак "минус" указывает, что вектор ускорения направлен противоположно вектору начальной скорости, что соответствует процессу торможения.

Ответ: ускорение поезда при торможении равно $-0.5$ м/с².

2. Дано:

Время, $t = 10$ с
Начальная скорость, $v_0 = 18$ км/ч
Конечная скорость, $v = 27$ км/ч

Переведем значения скоростей в систему СИ (м/с):
$v_0 = 18 \frac{км}{ч} = \frac{18 \cdot 1000 \text{ м}}{3600 \text{ с}} = 5 \text{ м/с}$
$v = 27 \frac{км}{ч} = \frac{27 \cdot 1000 \text{ м}}{3600 \text{ с}} = 7.5 \text{ м/с}$

Найти:

Ускорение, $a - ?$
Путь, $s - ?$

Решение:

Так как скорость изменяется равномерно, движение автомобиля является равноускоренным. Сначала определим ускорение по формуле:
$a = \frac{v - v_0}{t}$
Подставим числовые значения:
$a = \frac{7.5 \text{ м/с} - 5 \text{ м/с}}{10 \text{ с}} = \frac{2.5}{10} \frac{м}{с^2} = 0.25 \frac{м}{с^2}$
Далее найдем путь, пройденный автомобилем за это время. Для этого можно использовать формулу пути при равноускоренном движении:
$s = v_0 t + \frac{at^2}{2}$
Или более простую в данном случае формулу, использующую среднюю скорость:
$s = \frac{v + v_0}{2} \cdot t$
Подставим известные значения во вторую формулу:
$s = \frac{7.5 \text{ м/с} + 5 \text{ м/с}}{2} \cdot 10 \text{ с} = \frac{12.5}{2} \cdot 10 \text{ м} = 6.25 \cdot 10 \text{ м} = 62.5 \text{ м}$

Ответ: ускорение автомобиля равно $0.25$ м/с², а пройденный путь составляет $62.5$ м.

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