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Консультация № 198497
09.05.2020, 08:13
0.00 руб.
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
На графике показана зависимость проекции ускорения ax материальной точки, движущейся вдоль оси x, от времени t. Начальная проекция скорости точки vx (при t=0 с) равна 2 м/с. Чему будет равен модуль её скорости в момент времени t=5 с?
Спасибо
На графике показана зависимость проекции ускорения ax материальной точки, движущейся вдоль оси x, от времени t. Начальная проекция скорости точки vx (при t=0 с) равна 2 м/с. Чему будет равен модуль её скорости в момент времени t=5 с?
Спасибо
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Обсуждение
14.05.2020, 08:27
общий
это ответ
Здравствуйте, suvorov.shool@mail.ru!
Из условий задачи следует, что точка движется вдоль оси x, следовательно, её скорость и ускорение численно совпадает с проекциями на эту ось (v = v[sub]x[/sub] и a = a[sub]x[/sub]). В общем случае, если точка движется с ускорением a = a(t), зависящим от времени, то её скорость в момент времени t определяется выражением
где v[sub]0[/sub] - скорость в момент t = 0. В данном случае v[sub]0[/sub] = 2 м/с, из приведённого графика следует, что a(t) = 2t при 0 < t < 2 и a(t) = (t+22)/6 при t [$8805$] 2, поэтому
при t < 2 с, v(2) = 6 м/с и
при t > 2 с. В частности, при t = 5 с скорость (и её модуль) будет равна
м/с.
Из условий задачи следует, что точка движется вдоль оси x, следовательно, её скорость и ускорение численно совпадает с проекциями на эту ось (v = v[sub]x[/sub] и a = a[sub]x[/sub]). В общем случае, если точка движется с ускорением a = a(t), зависящим от времени, то её скорость в момент времени t определяется выражением
где v[sub]0[/sub] - скорость в момент t = 0. В данном случае v[sub]0[/sub] = 2 м/с, из приведённого графика следует, что a(t) = 2t при 0 < t < 2 и a(t) = (t+22)/6 при t [$8805$] 2, поэтому
при t < 2 с, v(2) = 6 м/с и
при t > 2 с. В частности, при t = 5 с скорость (и её модуль) будет равна
м/с.
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