A body is moving along a straight line under a force that delivers constant power.   Distance travelled by the body in time ‘t’ is proportional to

Power    P  =   F⋅v here F is force, v is velocity, given Power is constant ∴   constant   =    F. v     ∴     F α  1v ⇒m   a  α  1v m is mass, a is acceleration    a  α  1v ⇒dvdtα1v ⇒dvdtdxdxα1v x is displacement, t is time ⇒dxdtdvdxα1v ⇒   v⋅dvdx  α  1v ⇒v2.dv α dx integrating ⇒∫v2.dv α ∫dx ⇒v33 α x ⇒v3α x                           ⇒ v  α   x1/3                                     ⇒dxdt   α   x1/3⇒ ⇒dxx13   α    dt integrating ⇒∫dxx13   α∫    dt ⇒ x2/323 α t ⇒x2/3  α   t ⇒x   α   t3/2