Work energy Power doubt

Question

An object of mass m, initially at rest under the action of a constant force F attains a velocity v in time t.

Then the average power is supplied to mass is ?

Answer 1

Two ways to do this:

 

(1)

 

<P> = Δ(KE) / t = [(KE)₂ - (KE)₁] / t = [(1/2)mv² - (1/2)m(0)²] / t = (1/2)mv²/t

 

(2)

 

<P> = (P₁ + P₂) / 2 = [F(0) + Fv] / 2 = Fv/2 = [m(v - 0) / t] v/2 = (1/2)mv²/t