An inspection trolley is modelled as moving along a straight rail with velocity v=(12−2t2) m s−1v=(12-2t^2)\text{ m s}^{-1}v=(12−2t2) m s−1 for t≥0t\geq0t≥0.
Find the distance travelled in the first second.
Find the time at which the particle changes direction.
Find the first time at which the particle returns to its starting point.
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.