A particle has acceleration a=2t m s−2a=2t\text{ m s}^{-2}a=2t m s−2 for 0≤t≤20\leq t\leq20≤t≤2, and constant acceleration k m s−2k\text{ m s}^{-2}k m s−2 for 2<t≤52<t\leq52<t≤5. Its initial velocity is 1 m s-1 and its velocity at t=5t=5t=5 is -1 m s-1.
Determine kkk.
Determine the displacement during the first 5 seconds.
Determine the total distance travelled during the first 5 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.