A train starts from rest and accelerates uniformly at 2 m s-2 for T T\,T seconds. It then travels at constant speed for 10 seconds before decelerating uniformly at 1 m s-2 until it comes to rest. The total distance travelled is 128 m.
Show that 3T2+20T−128=03T^2+20T-128=03T2+20T−128=0.
Determine the value of TTT.
Find the total time for which the train is moving.
260 exam-style questions on OCR A Level Maths 3.2 Kinematics, covering 3.2.1 Language of kinematics, 3.2.2 Graphs in kinematics, 3.2.3 Displacement-time and velocity-time graphs, 3.2.4 Constant acceleration formulae, 3.2.5 Constant acceleration in two dimensions (A-level only), 3.2.6 Non-uniform acceleration in one dimension (A-level only), 3.2.7 Non-uniform acceleration in two dimensions (A-level only), 3.2.8 Motion under gravity using vectors (A-level only), and 3.2.9 Projectiles (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.