The acceleration of a particle travelling along a straight line is `a =(k)/(v)`, where `k` is constant `(k gt 0)`. If at `t=0,V=V_(0)` then speed of particle at `t = (V_(0)^(2))/(2)`.

Options

A. `V_(0)`
B. `(V_(0))/(2)`
C. `sqrt(3) V_(0)`
D. `sqrt(2)V_(0)`

Answer

C

Explanation

`(dV)/(dt)=(K)/(V)`
`underset(v_(0)) overset(v)(int) vdv =k underset(0) overset(k)(int) dt rArr V= sqrt(3) V_(0)`.