A car of mass 1200 kg is travelling along a straight horizontal road. The power of the car's engine is constant and is equal to 16 kW. There is a constant resistance to motion of magnitude 500 N.

(a) Find the acceleration of the car at an instant when its speed is 20 m/s.

(b) Assuming that the power and the resistance forces remain unchanged, find the steady speed at which the car can travel.

The car comes to the bottom of a straight hill of length 316 m, inclined at an angle to the horizontal of \(\sin^{-1}\left(\frac{1}{60}\right)\). The power remains constant at 16 kW, but the magnitude of the resistance force is no longer constant and changes such that the work done against the resistance force in ascending the hill is 128400 J. The time taken to ascend the hill is 15 s.

(c) Given that the car is travelling at a speed of 20 m/s at the bottom of the hill, find its speed at the top of the hill.