A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time ‘t’ is proportional to: 

   $P=maV p=m\times \frac{dv}{dt}v$
   $P=ma\frac{dv}{dx}v pdt=m.dv.v$
  $P\int dx=m\int v^2.dv p\int dt=m\int v.dv$ 
   $P.x=m\frac{v^3}{3} pt=\frac{m{v}^2}{2}$ 
 $x\alpha v^3 t\alpha v^2 x\alpha t^{3/2}$