A particle moving in a straight line is acted by a force, which works at a constant power and changes its velocity from u to v in passing over a distance x. The time taken will be:

The force acting on the particle =mdvdtPower of the force =mdvdtv=k (constant)mv22=kt+c …(1) at t=0,v=u∴c=mu22Now from (1),mv22=kt+mu2212mv2−u2=kt …(2) Again mdvdtv=km.vdvdxv=k∫0v mv2dv=∫0x kdxIntegrating,13mv3−u3=kx…(3)From eqn (2) and (3),t=32v2−u2v3−u3x