A particle has velocity v=((t−3)2+k) m s−1v=((t-3)^2+k)\text{ m s}^{-1}v=((t−3)2+k) m s−1, where k k\,k is a constant. During the first 6 seconds its displacement is 30 m.
Determine kkk.
Hence prove that the particle does not change direction.
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.