A constant power `P` is applied to a particle of mass `m`. The distance traveled by the particle when its velocity increases from `v_(1)` to `v_(2)` is (neglect friction):

Options

A. `3P/m(v_(2)^(2) - v_(1)^(2))`
B. `m/3P(v_(2) - v_(1))`
C. `m/3P(v_(2)^(3) - v_(1)^(3))`
D. `m/3P(v_(2)^(2) - v_(1)^(2))`

Answer

`(3)`

Explanation

`P = mav = m(dv)/(ds) v^(2), P/m int _(0)^(s) ds = int _(v_(1))^(v_(2)) v^(2) dv`