6 A car has mass 1250 kg .
- The car is moving along a straight level road at a constant speed of \(36 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and is subject to a constant resistance of magnitude 850 N . Find, in kW , the rate at which the engine of the car is working.
- The car travels at a constant speed up a hill and is subject to the same resistance as in part (i). The hill is inclined at an angle of \(\theta ^ { \circ }\) to the horizontal, where \(\sin \theta ^ { \circ } = 0.1\), and the engine is working at 63 kW . Find the speed of the car.
- The car descends the same hill with the engine of the car working at a constant rate of 20 kW . The resistance is not constant. The initial speed of the car is \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Eight seconds later the car has speed \(24 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and has moved 176 m down the hill. Use an energy method to find the total work done against the resistance during the eight seconds.