Assume that the engine of a car with mass m supplies a constantpower P to the wheels to accelerate the car. The car is initially at rest. Ignoring rolling friction and air resistance, (a) Show that the speed of the car is given as a function of time by v = (2Pt/m)^1/2. (b) Show that the acceleration of the car is not constant but is given as a function of time by a = (P/2mt)^1/2. (c) Show that the displacement is given by x-x0 = (8P/9m)^1/2t^3/2.