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June 2014 p43 q2
3457
A car of mass 1250 kg travels up a straight hill inclined at an angle \(\alpha\) to the horizontal, where \(\sin \alpha = 0.02\). The power provided by the car’s engine is 23 kW. The resistance to motion is constant and equal to 600 N. Find the speed of the car at an instant when its acceleration is \(0.5 \text{ m/s}^2\).
Solution
Using Newton's second law, the driving force \(DF\) is given by: