A particle has velocity v=7t−t2v=7t-t^2v=7t−t2 for 0≤t≤50\leq t\leq50≤t≤5, and v=20−2tv=20-2tv=20−2t for t>5t>5t>5, where v v\,v is measured in m s−1\text{m s}^{-1}m s−1.
Find the acceleration at t=4t=4t=4.
Find the total distance travelled during the first 10 seconds.
260 exam-style questions on OCR A Level Maths 3.2 Kinematics, covering 3.2.1 Language of kinematics, 3.2.2 Graphs in kinematics, 3.2.3 Displacement-time and velocity-time graphs, 3.2.4 Constant acceleration formulae, 3.2.5 Constant acceleration in two dimensions (A-level only), 3.2.6 Non-uniform acceleration in one dimension (A-level only), 3.2.7 Non-uniform acceleration in two dimensions (A-level only), 3.2.8 Motion under gravity using vectors (A-level only), and 3.2.9 Projectiles (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.