An automobile of mass m accelerates, starting from rest, with the engine supplying constant power 'P'. How the velocity of the automobile vary with time?
As Fv=P=constant
As F = mdvdt
i.e. mdvdtv = P
or
∫ vdv =∫pmdt
By integrating both sides we get v22=Pmt+C1
As initially the body is at rest i.e v = 0 at t=0, so C1=0 ∴ v=(2Ptm)12