A constant power `P` is applied to a partical of mass `m`. The distance travelled by the partical 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. `(3 p)/(m) (v_(2)^(2) - v_(1)^(2))`
D. `(m)/(3P) (v_(2)^(2) - v_(1)^(2))`

Answer

A

Explanation

`P = Fv = mav rArr a= (P)/(mv)`
` rArr (dv)/(ds)= (p)/(mv) rArr v^(2) dv = (P)/(m) dx `
`rArr (P)/(m) int _(0)^(s)ds= int_(v_(1))^(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)^(3))`