Two particles P P\,P and Q Q\,Q are moving in separate straight lines across a smooth horizontal surface.
P P\,P moves with constant velocity (3i+4j)(3\mathbf{i} + 4\mathbf{j})(3i+4j) m s−1^{-1}−1.
Q Q\,Q moves from the point with position vector (2i−5j)(2\mathbf{i} - 5\mathbf{j})(2i−5j) m to the point with position vector (20i+19j)(20\mathbf{i} + 19\mathbf{j})(20i+19j) m during a 3 second period.
Show that P P\,P and Q Q\,Q move along parallel lines.
Stevie says that Q Q\,Q is also moving with a constant velocity of (6i+8j)(6\mathbf{i} + 8\mathbf{j})(6i+8j) m s−1^{-1}−1. Explain why Stevie may be incorrect.
A third particle R R\,R moves with constant speed 5 m s−1^{-1}−1, in a straight line, across the same surface. P P\,P and R R\,R move along lines that intersect at a fixed point XXX. It is given that P P\,P passes through X X\,X exactly 2 seconds after R R\,R passes through XXX, and that P P\,P and R R\,R are exactly 510 5\sqrt{10}\,510 metres apart 3 seconds after R R\,R passes through XXX. Show that P P\,P and R R\,R move along perpendicular lines.
158 exam-style questions on OCR (MEI) A Level Maths 3.2 Kinematics, covering 3.2.1 Language of kinematics, 3.2.2 Position, displacement, distance and distance travelled, 3.2.3 Velocity, speed and acceleration distinctions, 3.2.4 Draw and interpret kinematics graphs, 3.2.5 Differentiate position and velocity (A-level only), 3.2.6 Integrate acceleration and velocity (A-level only), 3.2.7 When constant acceleration formulae apply, 3.2.8 Solve 1-D kinematics problems, 3.2.9 Language of kinematics in 2 dimensions (A-level only), 3.2.10 Extend 1-D techniques to 2-D using vectors (A-level only), 3.2.11 Cartesian equation of a path (A-level only), and 3.2.12 Vectors to solve kinematics problems (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.