3 The resistance to the motion of a car of mass 600 kg is \(k v \mathrm {~N}\), where \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) is the car's speed and \(k\) is a constant. The car ascends a hill of inclination \(\alpha\), where \(\sin \alpha = \frac { 1 } { 10 }\). The power exerted by the car's engine is 12000 W and the car has constant speed \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).

1. Show that \(k = 0.6\). The power exerted by the car's engine is increased to 16000 W .
2. Calculate the maximum speed of the car while ascending the hill. The car now travels on horizontal ground and the power remains 16000 W .
3. Calculate the acceleration of the car at an instant when its speed is \(32 \mathrm {~ms} ^ { - 1 }\).