An automated lift counterweight is modelled as a particle moving on a straight vertical line with acceleration a=(6t−12) m s−2a=(6t-12)\text{ m s}^{-2}a=(6t−12) m s−2. At t=0t=0t=0 its velocity is 9 m s-1 in the positive direction and its displacement from O O\,O is 4 m.
Find expressions for the velocity and displacement at time ttt.
Find the minimum value of the displacement for t≥0t\geq0t≥0.
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.