Engine switched off: find distance or speed

6 A van of mass 3200 kg travels along a horizontal road. The power of the van's engine is constant and equal to 36 kW , and there is a constant resistance to motion acting on the van.

1. When the speed of the van is \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), its acceleration is \(0.2 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). Find the resistance force.
   When the van is travelling at \(30 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), it begins to ascend a hill inclined at \(1.5 ^ { \circ }\) to the horizontal. The power is increased and the resistance force is still equal to the value found in part (i).
2. Find the power required to maintain this speed of \(30 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
3. The engine is now stopped, with the van still travelling at \(30 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), and the van decelerates to rest. Find the distance the van moves up the hill from the point at which the engine is stopped until it comes to rest.

2. A car of mass 500 kg is moving at a constant speed of \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) up a straight road inclined at an angle \(\theta\) to the horizontal, where \(\sin \theta = \frac { 1 } { 20 }\). The resistance to motion from non-gravitational forces is modelled as a constant force of magnitude 150 N .

1. Find the rate of working of the engine of the car. When the car is travelling up the road at \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the engine is switched off. The car then comes to instantaneous rest, without braking, having moved a distance \(d\) metres up the road from the point where the engine was switched off. The resistance to motion from non-gravitational forces is again modelled as a constant force of magnitude 150 N .
2. Use the work-energy principle to find the value of \(d\).