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

The force acting on the particle is given by
`F=F_0e^(-bt)`
`thereforea=F/m=(F_0e^(-bt))/m`
`therefore(dv)/(dt)=(F_0)/me^(-bt)`
`thereforedv=F_0/me^(-bt)dt`
Integrating both sides, we get
`int_0^bdv=int_0^tF_0/me^(-bt)dt`
`thereforev=F_0/m[e^(-bt)/-b]_0^t`
`thereforev=F_0/(mb)[e^(-bt)-(-e^0)]=F_0/(mb)[1-e^(-bt)]`
This is represented by the curve (b).