In this question you must show detailed reasoning.
The velocity-time graph of a particle consists of three parts. For 0≤t≤40\leq t\leq40≤t≤4, the velocity is v=k(t−2) m s−1v=k(t-2)\text{ m s}^{-1}v=k(t−2) m s−1. The particle then moves with constant velocity 2k m s−12k\text{ m s}^{-1}2k m s−1 until t=7t=7t=7. From t=7t=7t=7 to t=9t=9t=9, it decelerates uniformly to rest. The constant k k\,k is positive.
Sketch the velocity-time graph for 0≤t≤90\leq t\leq90≤t≤9.
State the acceleration during each of the three stages.
Given that the total distance travelled is 96 m, determine kkk.
Hence find the displacement of the particle during the nine 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.