A particle P P\,P moves with constant acceleration (3i−4j)(3\mathbf{i} - 4\mathbf{j})(3i−4j) m s−2^{-2}−2. When t=0t = 0t=0 the particle is at the origin O O\,O and is moving with velocity (2i−3j)(2\mathbf{i} - 3\mathbf{j})(2i−3j) m s−1^{-1}−1.
Find the velocity of P P\,P at time t=5t = 5t=5 s.
At time t=Tt = Tt=T seconds, where T>0T > 0T>0, P P\,P passes through the point AAA. The position vector of A A\,A is (ki−14j)(k\mathbf{i} - 14\mathbf{j})(ki−14j) m relative to OOO, where k k\,k is a constant. Find the value of TTT.
Hence find the value of kkk.
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.