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.
8 exam-style questions on OCR A Level Maths 3.2.3 Displacement-time and velocity-time graphs. Each one has a worked solution and a mark scheme showing where the marks go.