A particle P P\,P moves with constant velocity (3i+2j)(3\mathbf{i} + 2\mathbf{j})(3i+2j) m s−1^{-1}−1 relative to a fixed origin OOO. At time t=0t = 0t=0 it passes through the point AAA, whose position vector is (2i+11j)(2\mathbf{i} + 11\mathbf{j})(2i+11j) m.
Find the angle, in degrees, that the velocity of P P\,P makes with the vector i\mathbf{i}i.
Find the distance of P P\,P from O O\,O when t=2t = 2t=2 s.
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.