A particle has velocity v=(12−2t2) m s−1v=(12-2t^2)\text{ m s}^{-1}v=(12−2t2) m s−1 at time t t\,t seconds, where t≥0t\geq0t≥0. At t=0t=0t=0 the particle is at OOO.
Find the distance travelled in the first second.
Find the time at which the particle changes direction.
Find the next time at which the particle returns to OOO.
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.