1.85: Displacement-time graph and harmonic motion

0606/13/O/N/20 — Question 4 · 7 marks

1.85 diagram
The diagram shows the xx-tt graph for a runner, where displacement, xx, is measured in metres and time, tt, is measured in seconds.
(a)(i)
On the axes below, draw the vv-tt graph for the runner.
[3]
(a)(ii)
Find the total distance covered by the runner in 125125 s.
[1]
(b)
The displacement, xx m, of a particle from a fixed point at time tt s is given by x=6cos⁡(3t+π3)x = 6\cos\left(3t + \dfrac{\pi}{3}\right). Find the acceleration of the particle when t=2π3t = \dfrac{2\pi}{3}.
[3]