Power from work done over time (P = W/t)

1 A lorry of mass 16000 kg is travelling along a straight horizontal road. The engine of the lorry is working at constant power. The work done by the driving force in 10 s is 750000 J .

1. Find the power of the lorry's engine.
2. There is a constant resistance force acting on the lorry of magnitude 2400 N . Find the acceleration of the lorry at an instant when its speed is \(25 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).

2 A block is being pulled along a horizontal floor by a rope inclined at \(20 ^ { \circ }\) to the horizontal. The tension in the rope is 851 N and the block moves at a constant speed of \(2.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).

1. Show that the work done on the block in 12 s is approximately 24 kJ .
2. Hence find the power being applied to the block, giving your answer to the nearest kW .

7 Find the power required to pump \(3 \mathrm {~m} ^ { 3 }\) of water per minute from a depth of 25 m and deliver it through a circular pipe of diameter 10 cm . Assume that friction may be neglected and that the density of water is \(1000 \mathrm {~kg} \mathrm {~m} ^ { - 3 }\).

Use \(g\) as 9.8 m s\(^{-2}\) in this question. A pump is used to pump water out of a pool. The pump raises the water through a vertical distance of 5 metres and then ejects it through a pipe. The pump works at a constant rate of 400 W Over a period of 50 seconds, 300 litres of water are pumped out of the pool and the water is ejected with speed \(v\) m s\(^{-1}\) The mass of 1 litre of water is 1 kg

1. Find the gain in the potential energy of the 300 litres of water. [1 mark]
2. Calculate \(v\) [4 marks]