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 \(15 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the acceleration of the car is \(0.2 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).

1. Show that \(R = 600\). The car now moves with constant speed \(U \mathrm {~m} \mathrm {~s} ^ { - 1 }\) downhill on a straight road inclined at \(\theta\) to the horizontal, where \(\sin \theta = \frac { 1 } { 40 }\). 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.
2. Calculate the value of \(U\).
   (5)