A particle of mass m is driven by a machine that delivers a constant power k watts. If the particle starts from rest the force on the particle at time t is

Power k = F.v = (ma)v = mdvdt v = mvdvdtRearranging we get, vdv = kmdtIntegrating both side,∫0vvdv = km∫0tdt     ⇒ v22 = kmt⇒v = 2 ktm---------------(i)Force acting on particle F = mdvdt------(ii)Differentiating equation (i) w.r.t timedvdt = (2km)dt-12d = (2km)12t-12 = (k2m)t-12Substituting the value of dvdt in equation (ii) we getF = mdvdt = m(k2m)t-12 = (mk2t-12)