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

Explanation

Power P = F.v = (ma) v = `a = (P)/(mv) rArr v.(dv)/(ds) = (P)/(mv)` `v^(2).dv=(P)/(m)ds " " (P)/(m)underset(0)overset(s)intds=underset(v_(1))overset(v_(2))intv^(2).dv`
`(P)/(m)s=(1)/(3)(v_(2)^(3)-v_(1)^(3))" " therefores=(m)/(3p)(v_(2)^(3)-v_(1)^(3))`