An object of mass m starts from rest and is driven by an engine that delivers a constant power P . The velocity v of the object varies with time t as:

Step-by-step solution

The power P delivered by the engine is constant. Power is given by the product of force and velocity: P = Fv According to Newton's second law, F = m dv dt , so: P = (m dv dt ) v v dv = P m dt Integrating both sides from t = 0 (where v = 0 ) to time t : ₀^v v dv = ₀^t P m dt v^2 2 = P m t v = 2P m t^ 1/2 Since P and m are constants, the velocity is proportional to t^ 1/2 ( v t^ 1/2 ). Assuming constant force instead of constant power would incorrectly lead to v t . Answer: v t^ 1/2