Forces acting on a particle moving in a straight line varies with the velocity of the particle as `F = (alpha)/(upsilon)` where `alpha` is constant. The work done by this force in time interval `Delta t` is :

Options

A. KVt
B. `K^2V^2t^2`
C. `K^2Vt`
D. `(3Kt)/(2V)`

Answer

D

Explanation

`m(dv)/(dt)=Kv^(-2)`
`etam(v^2dv)=etaKdt`
`m((v^3)/(3))=Kt`
`1/2mv^2=3/2(Kt)/(v)`