A train accelerates from rest at station A to a velocity of k m s−1k\text{ m s}^{-1}k m s−1, where k>0k>0k>0. It maintains this speed for 72 seconds, until it decelerates uniformly to station B. The total journey time is 112 seconds and the magnitudes of the acceleration and deceleration are equal.
Find:
the time it takes the train to accelerate from rest to k m s−1k\text{ m s}^{-1}k m s−1.
sketch a velocity-time graph for the motion of the train between station A and station B.
calculate the distance between the two stations in terms of kkk.
36 exam-style questions on Edexcel A Level Maths 9.2 Velocity-Time Graphs. Each one has a worked solution and a mark scheme showing where the marks go.