| Date | May 2017 | Marks available | 2 | Reference code | 17M.1.hl.TZ2.4 |
| Level | HL only | Paper | 1 | Time zone | TZ2 |
| Command term | Find | Question number | 4 | Adapted from | N/A |
Question
A particle moves along a straight line. Its displacement, \(s\) metres, at time \(t\) seconds is given by \(s = t + \cos 2t,{\text{ }}t \geqslant 0\). The first two times when the particle is at rest are denoted by \({t_1}\) and \({t_2}\), where \({t_1} < {t_2}\).
Find \({t_1}\) and \({t_2}\).
Find the displacement of the particle when \(t = {t_1}\)
Markscheme
\(s = t + \cos 2t\)
\(\frac{{{\text{d}}s}}{{{\text{d}}t}} = 1 - 2\sin 2t\) M1A1
\( = 0\) M1
\( \Rightarrow \sin 2t = \frac{1}{2}\)
\({t_1} = \frac{\pi }{{12}}(s),{\text{ }}{t_2} = \frac{{5\pi }}{{12}}(s)\) A1A1
Note: Award A0A0 if answers are given in degrees.
[5 marks]
\(s = \frac{\pi }{{12}} + \cos \frac{\pi }{6}\,\,\,\left( {s = \frac{\pi }{{12}} + \frac{{\sqrt 3 }}{2}(m)} \right)\) A1A1
[2 marks]
