The speed v reached by a car of mass m in travelling a distance x, driven with constant power P, is given by

powere =P= Fv here F is force, v is velocity, and F= ma, here a is accelerationP =m dvdt v, here differential form of acceleration is consideredor    v dvdt=  Pmor   v dvdxdxdt=Pm , here in left hand side , divide and multiply by dx,or  v2dvdx=Pm  or   v2dv=Pmdx ∫v2dv=∫PmdxOn integration , we get v33=Pxm  or  v =  3xPm13