M2 January 2006 Q3

3. A car of mass 1000 kg is moving along a straight horizontal road. The resistance to motion is modelled as a constant force of magnitude \(R\) newtons. The engine of the car is working at a rate of 12 kW. When the car is moving with speed 15 m s\(^{-1}\), the acceleration of the car is 0.2 m s\(^{-2}\).

The car now moves with constant speed \(U\) m s\(^{-1}\) downhill on a straight road inclined at \(\theta\) to the horizontal, where \(\sin\theta = \tfrac{1}{40}\). The engine of the car is now working at a rate of 7 kW. The resistance to motion from non-gravitational forces remains of magnitude \(R\) newtons.