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

C

Explanation

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