A particle P P\,P moves in a straight line so that, at time t t\,t seconds, its velocity v m s−1v \text{ m s}^{-1}v m s−1 is given by
v={7t−t20≤t≤510−2tt>5 v = \begin{cases} 7t - t^2 & 0 \leq t \leq 5 \\ 10 - 2t & t > 5 \end{cases} v={7t−t210−2t0≤t≤5t>5Find the acceleration of P P\,P when t=4t = 4t=4
Find the total distance traveled by P P\,P in the first 10 seconds.
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.