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Консультация № 180144
03.10.2010, 22:37
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Расстояние 20 км между двумя станциями поезд проходит со скоростью, средний модуль которой равен 72 км/ч, причем на разгон он тратит 2 мин, а затем идет с постоянной скоростью. На торможение до полной остановки он тратит 3 минуты. Определите модуль максимальной скорости поезда.
Обсуждение
04.10.2010, 06:38
общий
это ответ
Здравствуйте, Посетитель - 338609.
Решаю задачу исходя из предположения, что разгон и торможение происходят равномерно.
Средняя скорость - есть отношение всего пути ко всему времени, тогда имеем:
Vср=S/t
t=S/Vср=20000/20=1000 (с)
Дальше проще всего решать графически: график V(t) - трапеция, площадь которой равна расстоянию S. Эта площадь считается обычной геометрической формулой:
S = (t+(t - t1 - t2))*Vmax/2
Выразим искомую величину:
Vmax=2*S/(t+(t - t1 - t2))
Вычислим искомую величину:
Vmax=2*20000/(1000+(1000 - 120 - 180))[$8776$]23.5 (м/с)
Решаю задачу исходя из предположения, что разгон и торможение происходят равномерно.
Средняя скорость - есть отношение всего пути ко всему времени, тогда имеем:
Vср=S/t
t=S/Vср=20000/20=1000 (с)
Дальше проще всего решать графически: график V(t) - трапеция, площадь которой равна расстоянию S. Эта площадь считается обычной геометрической формулой:
S = (t+(t - t1 - t2))*Vmax/2
Выразим искомую величину:
Vmax=2*S/(t+(t - t1 - t2))
Вычислим искомую величину:
Vmax=2*20000/(1000+(1000 - 120 - 180))[$8776$]23.5 (м/с)
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