M1 June 2009 Q1

1. Three posts \(P\), \(Q\) and \(R\), are fixed in that order at the side of a straight horizontal road. The distance from \(P\) to \(Q\) is 45 m and the distance from \(Q\) to \(R\) is 120 m. A car is moving along the road with constant acceleration \(a\) m s\(^{-2}\). The speed of the car, as it passes \(P\), is \(u\) m s\(^{-1}\). The car passes \(Q\) two seconds after passing \(P\), and the car passes \(R\) four seconds after passing \(Q\). Find