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A particle of mass m is at rest at the o...

A particle of mass m is at rest at the origin at time t = 0.It is subjected to a force `F(t)=F_(0)e^(-bt)` in the x direction. Its speed v(t) is depicted by which of the following curves ?

A

B

C

D

Text Solution

Verified by Experts

The correct Answer is:
D
`F=ma=F_(0)e^(-bt)`
`(dv)/(dt)=(F_(0))/(m)e^(-bt)`
`underset(0)overset(v)int dv=(F_(0))/(m)underset(0)overset(t)int e^(-bt)dt=(F_(0))/(m)((e^(-bt))/(-b))_(0)^(t)`
`v=(F_(0))/(mb)(1-e^(-bt))`
So, correct choice is (d).
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