A Body is moved along a straight line by a machine delivering a constant power.  The distance moved by the Body in time ‘t’ is proportional to

power P=worktime  P =    F⋅St   P=    F⋅V P=force . velocity  given P=  F⋅V    = constant let constant =K F.V=K we know F =ma and velocity = accelerationtime, substitute in above equationm⋅a⋅  at   =    K      ⇒     a  =    (Kmt)12---(!)   displacement    S=       12 at2 substitute equation (1)   ⇒    S  =    12 a(Kmt)12   t2                          ⇒    S  =    12 (Km)12   t32                                ∴   S  α t32