4 A lorry of mass 16000 kg climbs from the bottom to the top of a straight hill of length 1000 m at a constant speed of \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The top of the hill is 20 m above the level of the bottom of the hill. The driving force of the lorry is constant and equal to 5000 N . Find

1. the gain in gravitational potential energy of the lorry,
2. the work done by the driving force,
3. the work done against the force resisting the motion of the lorry. On reaching the top of the hill the lorry continues along a straight horizontal road against a constant resistance of 1500 N . The driving force of the lorry is not now constant, and the speed of the lorry increases from \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at the top of the hill to \(25 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at the point \(P\). The distance of \(P\) from the top of the hill is 2000 m .
4. Find the work done by the driving force of the lorry while the lorry travels from the top of the hill to \(P\).