A particle of mass m moving along a straight line is acted on by (always directed against the motion) `F-be^(alphav)` where b and `alpha` are postive constants and x is the velocity. At t-0 it is moving with velocity `V_(0)`. At what time does it come to rest?

Options

A. `(m)/(alpha b)(1-e^(-alphav_(0)))`
B. `(m)/(alphab)(e^(alphav_(0)-1))`
C. `(m)/(alphab)e`
D. `(m)/(alphab)e^(-alphav_(0)`

Explanation

`m(dv)/(dt)=-be^(+av)`
`rArr int_(v_(0))^(0)e^(-av)d(-v)=int_(0)^(t_(0))(b)/(m)dt`
`e^(av_(0))-1=(bt)/(m)`