A lorry of mass 16000 kg travels at constant speed from the bottom, O, to the top, A, of a straight hill. The distance OA is 1200 m and A is 18 m above the level of O. The driving force of the lorry is constant and equal to 4500 N.

1. Find the work done against the resistance to the motion of the lorry.

On reaching A the lorry continues along a straight horizontal road against a constant resistance of 2000 N. The driving force of the lorry is not now constant, and the speed of the lorry increases from 9 m/s at A to 21 m/s at the point B on the road. The distance AB is 2400 m.

2. Use an energy method to find F, where F N is the average value of the driving force of the lorry while moving from A to B.
3. Given that the driving force at A is 1280 N greater than F N and that the driving force at B is 1280 N less than F N, show that the power developed by the lorry’s engine is the same at B as it is at A.