A constant power .P. is applied to a particle of mass .m.. The displacement of the particle when its velocity increases from `upsilon_(1)` to `upsilon_(2)` is (ignore friction)

Explanation

Power P = F. `upsilon = (ma)upsilon`
`a=(P)/(m upsilon) rArr upsilon(d upsilon)/(ds)=(P)/(m upsilon)`
`upsilon^(2).d upsilon=(P)/(m)" ds " (P)/(m) int_(0)^(s) ds = int_(upsilon_(1))^(upsilon_(2))upsilon^(2).d upsilon`
`(P)/(m).s=(1)/(3)(upsilon_(2)^(3)-upsilon_(1)^(3)) " " therefore s=(m)/(3P)(upsilon_(2)^(3)-upsilon_(1)^(3))`