A car has mass 550 kg . When the car travels along a straight horizontal road there is a constant resistance to the motion of magnitude \(R\) newtons, the engine of the car is working at a rate of \(P\) watts and the car maintains a constant speed of \(30 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). When the car travels up a line of greatest slope of a hill which is inclined at \(\theta\) to the horizontal, where \(\sin \theta = \frac { 1 } { 14 }\), with the engine working at a rate of \(P\) watts, it maintains a constant speed of \(25 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The non-gravitational resistance to motion when the car travels up the hill is a constant force of magnitude \(R\) newtons.
(i) Find the value of \(R\).
(ii) Find the value of \(P\).
Find the acceleration of the car when it travels along the straight horizontal road at \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) with the engine working at 50 kW .