A car of mass 1200 kg is travelling along a horizontal road.

(i) It is given that there is a constant resistance to motion.

(a) The engine of the car is working at 16 kW while the car is travelling at a constant speed of 40 m s^-1. Find the resistance to motion.

(b) The power is now increased to 22.5 kW. Find the acceleration of the car at the instant it is travelling at a speed of 45 m s^-1.

(ii) It is given instead that the resistance to motion of the car is (590 + 2v) N when the speed of the car is v m s^-1. The car travels at a constant speed with the engine working at 16 kW. Find this speed.