The unit vectors i\mathbf{i}i and j\mathbf{j}j are due east and due north respectively.
A boat B B\,B moves with constant velocity. At noon, B B\,B is at the point with position vector (2i−5j)(2\mathbf{i} - 5\mathbf{j})(2i−5j) km relative to a fixed origin OOO. At 1430, B B\,B is at the point with position vector (−8i+10j)(-8\mathbf{i} + 10\mathbf{j})(−8i+10j) km.
Find the velocity of BBB.
Find the bearing on which B B\,B is travelling.
Find an expression, in terms of ttt, for the position vector of B B\,B at t t\,t hours after noon.
265 exam-style questions on AQA A Level Maths 3.2 Q: Kinematics, covering 3.2.1 Language of kinematics, 3.2.2 Graphs in kinematics, 3.2.3 Constant acceleration formulae, 3.2.4 Calculus in kinematics (A-level only), and 3.2.5 Motion under gravity and projectiles (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.