A test carriage is modelled as moving along a straight track. At time t t\,t seconds its velocity is v=(kt+5−2t2) m s−1v=(kt+5-2t^2)\text{ m s}^{-1}v=(kt+5−2t2) m s−1, where k k\,k is a positive constant. The carriage stops accelerating when t=3t=3t=3.
Find kkk.
Find the distance of the particle from its starting point when it first changes direction.
158 exam-style questions on OCR (MEI) A Level Maths 3.2 Kinematics, covering 3.2.1 Language of kinematics, 3.2.2 Position, displacement, distance and distance travelled, 3.2.3 Velocity, speed and acceleration distinctions, 3.2.4 Draw and interpret kinematics graphs, 3.2.5 Differentiate position and velocity (A-level only), 3.2.6 Integrate acceleration and velocity (A-level only), 3.2.7 When constant acceleration formulae apply, 3.2.8 Solve 1-D kinematics problems, 3.2.9 Language of kinematics in 2 dimensions (A-level only), 3.2.10 Extend 1-D techniques to 2-D using vectors (A-level only), 3.2.11 Cartesian equation of a path (A-level only), and 3.2.12 Vectors to solve kinematics problems (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.