M2 June 2015 Q1

1. A van of mass 900 kg is moving down a straight road that is inclined at an angle \(\theta\) to the horizontal, where \(\sin\theta = \dfrac{1}{30}\). The resistance to motion of the van has constant magnitude 570 N. The engine of the van is working at a constant rate of 12.5 kW.

At the instant when the van is moving down the road at 5 m s\(^{-1}\), the acceleration of the van is \(a\) m s\(^{-2}\).

Find the value of \(a\). (5)