5 A lorry of mass 16000 kg travels at constant speed from the bottom, \(O\), to the top, \(A\), of a straight hill. The distance \(O A\) 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 \(9 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at \(A\) to \(21 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at the point \(B\) on the road. The distance \(A B\) is 2400 m .
2. Use an energy method to find \(F\), where \(F \mathrm {~N}\) 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 \(F \mathrm {~N}\) and that the driving force at \(B\) is 1280 N less than \(F \mathrm {~N}\), show that the power developed by the lorry's engine is the same at \(B\) as it is at \(A\).