Particle P P\,P passes a point O O\,O with speed 6 m s-1 and then moves along a straight line with constant acceleration 2 m s-2. Four seconds later, particle Q Q\,Q passes O O\,O moving in the same direction with constant speed 30 m s-1.
Let t t\,t seconds be the time after P P\,P passes OOO.
Show that, when the particles are at the same point, t2−24t+120=0t^2-24t+120=0t2−24t+120=0.
Hence show that Q Q\,Q overtakes P P\,P twice.
Determine the distance from O O\,O at which Q Q\,Q first overtakes PPP.
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.