A particle P P\,P moves with a constant velocity (2i+5j) ms−1(2\mathbf{i} + 5\mathbf{j}) \text{ ms}^{-1}(2i+5j) ms−1 with respect to a fixed origin OOO. It passes through the point A A\,A whose position vector is (4i−4j) m(4\mathbf{i} - 4\mathbf{j}) \text{ m}(4i−4j) m at t=0t = 0t=0.
Find the angle in degrees that the velocity vector of P P\,P makes with the vector i\mathbf{i}i.
Calculate the distance of P P\,P from O O\,O when t=4t = 4t=4.
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.