A particle is projected from a point O O\,O along a straight horizontal line with speed k m s−1k\text{ m s}^{-1}k m s−1, where k>0k>0k>0. It moves with constant acceleration -2 m s-2 until it returns to OOO. The greatest displacement of the particle from O O\,O is 36 m.
Show that the time at which the particle changes direction is k2\dfrac{k}{2}2k seconds.
Determine the value of kkk.
Find the total time taken for the particle to return 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.