M1 January 2012 Q6

6. A car moves along a straight horizontal road from a point \(A\) to a point \(B\), where \(AB = 885\) m. The car accelerates from rest at \(A\) to a speed of 15 m s\(^{-1}\) at a constant rate \(a\) m s\(^{-2}\). The time for which the car accelerates is \(\tfrac{1}{3}T\) seconds. The car maintains the speed of 15 m s\(^{-1}\) for \(T\) seconds. The car then decelerates at a constant rate of 2.5 m s\(^{-2}\) stopping at \(B\).