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

Options

A.
B.
C.
D.

Answer

C

Explanation

`a=(du)/(dt)=(F_(0)e^(-bt))/m`
`rArr underset(0)overset(u)intdu=F_(0)/m underset(0)overset(t)inte^(-bt)dt`
`u=F_(0)/m|e^(-bt)/(-b)|_(0)^(t)=F_(0)/(mb)(e^(-bt)-1)`