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

Answer

A

Explanation

`P=F_(v) =mav rArr a=(P)/(mv)`
`rArr v(dv)/(ds) =(P)/(mv) rArr v^(2) dv =(P)/(m) ds`
`rArr (P)/(m) int_(0)^(s) ds =int_(v1)^(v2)v^(2) dv rArr (P)/(m) s =(1)/(3) (v_(2)^(3) -v_(1)^(3))`
`rArr s=(m)/(3P) (v_(2)^(3) -v_(1)^(2))`.