A cyclist and his bicycle have a total mass of 75 kg . The cyclist is moving up a straight road inclined at an angle \(\theta\) to the horizontal, where \(\sin \theta = \frac { 1 } { 21 }\). The non-gravitational resistance to motion is modelled as a constant force of magnitude \(R\) newtons. The cyclist is working at a constant rate of 280 W and moving at a constant speed of \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
Find the value of \(R\).
Later the cyclist cycles down the same road on the same bicycle. He is again working at a constant rate of 280 W and the resistance to motion is now modelled as a constant force of magnitude 60 N .
Find the acceleration of the cyclist at the instant when his speed is \(3.5 \mathrm {~ms} ^ { - 1 }\).