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Задать вопрос экспертам

Консультация № 199266

06.10.2020, 18:32

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0 1 1

Образование

Здравствуйте! Прошу помощи в следующем вопросе:

Частица начала свое движение из начала координат с начальной скоростью V0 = (i - j)*A и с ускорением, которое зависит от времени по закону а (t) = j * B t/ τ, где А, В - постоянная величина, i, j - единичные орты в декартовой системе координат. Каков модуль скорости частицы в момент времени t = 1 c, если τ = 1 c.

Заранее спасибо.

Обсуждение

давно

Roman Chaplinsky / Химик CH

Модератор
156417
2175

08.10.2020, 20:24

общий

это ответ

Здравствуйте, savelev.perm.bio!

Чтобы найти скорость (векторную!), проинтегрируем ускорение и сложим с начальной скоростью
v^[$8594$]=v₀^[$8594$]+₀^t[$8747$]a(t)dt=A(i^[$8594$]-j^[$8594$])+(B/[$964$])j^[$8594$]₀^t[$8747$]tdt=
=i^[$8594$][$183$]A+j^[$8594$][$183$](Bt²/2[$964$]-A)
v^[$8594$](t=1с)=i^[$8594$][$183$]A+j^[$8594$][$183$](B/2-A)
модуль скорости
v=[$8730$](A²+(B/2-A)²)=[$8730$](2A²-AB+B²/4)

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