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Консультация № 172797
01.10.2009, 09:05
0.00 руб.
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1
1
Здравствуйте, уважаемые эксперты! Пожалуйста, помогите решить задачу.
1. Кинематика
1. 17. Зависимость пройденного телом пути от времени задается уравнением s = А + Bt + Ct2 + Dt3 (С = 0,1 м/с2, D = 0,03 м/с3). Определить: 1) через сколько времени после начала движения ускорение а тела будет равно 2 м/с2; 2) среднее ускорение <а> тела за этот промежуток времени.
Нужно решение. . .
Ответ: 1) 10 с; 2) 1,1 м/с2.
1. Кинематика
1. 17. Зависимость пройденного телом пути от времени задается уравнением s = А + Bt + Ct2 + Dt3 (С = 0,1 м/с2, D = 0,03 м/с3). Определить: 1) через сколько времени после начала движения ускорение а тела будет равно 2 м/с2; 2) среднее ускорение <а> тела за этот промежуток времени.
Нужно решение. . .
Ответ: 1) 10 с; 2) 1,1 м/с2.
Обсуждение
Неизвестный
01.10.2009, 09:53
общий
01.10.2009, 10:39
это ответ
Здравствуйте, kot31.
1) Ускорение тела равно двойной производной от уравнения пройденного пути: а=d2s/dt2=(A+Bt+Ct2+Dt3)"=2C+6Dt
Отсюда t=(a-2C)/6D=(2-2*0,1)/(6*0,03)=10 c.
2)Среднее ускорение рано изменение скорости за этот промежуток времени деленное на этот промежуток времени: <a>=(v-v0)/t
Скорость равна производной от уравнения пройденного пути: v=ds/dt=(A+Bt+Ct2+Dt3)'=B+2Ct+3Dt2
При t=0 v0=B
t=10 с v=B+2*0,1*10+3*0,03*102=B+11
<a>=(B+11-B)/10=1,1 м/с2.
1) Ускорение тела равно двойной производной от уравнения пройденного пути: а=d2s/dt2=(A+Bt+Ct2+Dt3)"=2C+6Dt
Отсюда t=(a-2C)/6D=(2-2*0,1)/(6*0,03)=10 c.
2)Среднее ускорение рано изменение скорости за этот промежуток времени деленное на этот промежуток времени: <a>=(v-v0)/t
Скорость равна производной от уравнения пройденного пути: v=ds/dt=(A+Bt+Ct2+Dt3)'=B+2Ct+3Dt2
При t=0 v0=B
t=10 с v=B+2*0,1*10+3*0,03*102=B+11
<a>=(B+11-B)/10=1,1 м/с2.
5
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