Calculating Power with Constant Force: Deriving P=(F^2t)/m from Newton's 2nd Law

[dch1runs]

A particle of mass m moves from rest at t=0 under the influence of a single constant force F. Show that the power delivered by the force at any time t is P=(F^2t)/m.
I tried using the definition of power and the definition of the scalar product, which probably is not the way to go about doing this. I feel like there's an obvious step or equation that I'm missing here.

P=F.v=|F||v|cos0=Fv
mv(dv/dt)=P

 

[PhanthomJay]

using P =Fv is good. Now you need to find v as a function of F, T, and m using Newton's 2nd law (and the kinematic motion equations if it doesn't jump right out at you).