A particle of mass m moving along a straight line is acted on by a retrading force (always directed against the motion) `F=be^(alphav)`, where b abd `alpha` are positive constant and v 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^(alphav_(0))`
D. `m/(alphav)e^(-alphav_(0))`

Answer

1

Explanation

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