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Консультация № 200119
19.01.2021, 21:54
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Зависимость модуля ускорения частицы от времени имеет вид: a(t)=1-2t+3t2 (t в квадрате) (м/c2). Если в момент времени t0=0 модуль скорости частицы v0=0, то в момент времени t1=1c, модуль скорости частицы будет равен… м/c.
Зависимость модуля ускорения частицы от времени имеет вид: a(t)=1-2t+3t2 (t в квадрате) (м/c2). Если в момент времени t0=0 модуль скорости частицы v0=0, то в момент времени t1=1c, модуль скорости частицы будет равен… м/c.
Обсуждение
20.01.2021, 00:48
общий
это ответ
Здравствуйте, Ника!
Дано:
a(t)=1-2t+3t2 (м/с2)
vo=0
t1=1c
v1-?
Решение:
Ускорение - производная скорости по времени, значит скорость найдем интегрируя ускорение:
v(t)=[$8747$]a(t)dt
v(t)=t-t2+t3 (м/с)
v1=v(t1)=1-12+13=1 м/с
Дано:
a(t)=1-2t+3t2 (м/с2)
vo=0
t1=1c
v1-?
Решение:
Ускорение - производная скорости по времени, значит скорость найдем интегрируя ускорение:
v(t)=[$8747$]a(t)dt
v(t)=t-t2+t3 (м/с)
v1=v(t1)=1-12+13=1 м/с
Об авторе:
С уважением
shvetski
С уважением
shvetski
20.01.2021, 01:18
общий
Спасибо большое! Но почему-то в тесте такого ответа нет...
Прикрепленные файлы:
20.01.2021, 11:30
общий
20.01.2021, 11:34
Адресаты:
Давайте, проверим...
Интегрируем функцию а(t)
v=[$8747$](1-2t+3t2)dt=
= [$8747$]1 + (-2)[$8747$]t + 3[$8747$]t2 =
t - 2t2/2 + 3t3/3 =
t-t2+t3... ну, и далее, как в решении...
Давайте для проверки возьмем производную от скорости
a=dv/dt=d(t-t2+t3)/dt = 1 - 2t + 3t2 - вроде, все попадает, как надо...
боюсь я вам не смогу предложить другого ответа
, может кто-то из коллег найдет здесь какую-то математическую хитрость, которую я не вижу
sorry
Об авторе:
С уважением
shvetski
С уважением
shvetski
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