1. A car has a mass of 800 kg . The engine of the car is working at a constant power of 15 kW .

In an initial model of the motion of the car it is assumed that the car is subject to a constant resistive force of magnitude \(R \mathrm {~N}\). The car is initially driven on a straight horizontal road. At the instant that its speed is \(20 \mathrm {~ms} ^ { - 1 }\) its acceleration is \(0.4 \mathrm {~ms} ^ { - 2 }\).

1. Show that \(R = 430\).
2. Hence find the maximum constant speed at which the car can be driven along this road, according to the initial model. In a revised model the resistance to the motion of the car at any instant is assumed to be \(60 v\) where \(v\) is the speed of the car at that instant. The car is now driven up a straight road which is inclined at an angle \(\alpha\) above the horizontal where \(\sin \alpha = 0.2\).
3. Determine the speed of the car at the instant that its acceleration is \(0.15 \mathrm {~ms} ^ { - 2 }\) up the slope, according to the revised model.