The velocity-time graph of a particle consists of straight-line segments joining the points (0,4)(0,4)(0,4), (3,10)(3,10)(3,10), (7,10)(7,10)(7,10) and (12,−5)(12,-5)(12,−5), where time is measured in seconds and velocity in m s−1\text{m s}^{-1}m s−1.
Find the acceleration of the particle during the final 5 s.
Find the displacement of the particle in the first 12 s.
Find the total distance travelled in the first 12 s.
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.