A small aircraft P P\,P moves with a constant velocity. At 09:30, P P\,P is at the point with position vector (10i−5j) km(10\mathbf{i} - 5\mathbf{j}) \text{ km}(10i−5j) km with respect to a fixed origin OOO. At 12:00, the aircraft is at the point with position vector (−5i+25j) km(-5\mathbf{i} + 25\mathbf{j}) \text{ km}(−5i+25j) km.
Find the velocity of PPP.
Find the bearing of the velocity vector.
Find an expression, in terms of ttt, for the position of PPP t t\,t hours after 09:30.
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.