A car of mass 1200 kg moves up a straight road. The road is inclined to the horizontal at an angle \(\alpha\) where \(\sin \alpha = \frac { 1 } { 15 }\). The car is moving up the road with constant speed \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and the engine of the car is working at a constant rate of 11760 watts. The non-gravitational resistance to motion has a constant magnitude of \(R\) newtons.
Find the value of \(R\).
The rate of working of the car is now increased to 50 kW . At the instant when the speed of the car is \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the magnitude of the non-gravitational resistance to the motion of the car is 700 N and the acceleration of the car is \(1.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).