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

B

Explanation

`F=F_(0)Ee^(-bt)`
`a=(F)/(m)=(F_(0))/(m)e^(-bt)`
`(dv)/(dt)=(F_(0))/(m)e^(-bt)`
`int_(0)^(v)dv=(F_(0))/(m)int_(0)^(t)e^(-bt)dt`
`v=(F_(0))/(m)|e^(-bt)|_(0)^(t)/(-b)`
`v=(F_(0))/(mb)(1-e^(-bt))`
t=0,v=0
`t=oo,v=(F_(0))/(mb)`