Find ${t_1}$ and ${t_2}$.

Find the displacement of the particle when $t = {t_1}$

$s = t + \cos 2t$

$\frac{{{\text{d}}s}}{{{\text{d}}t}} = 1 - 2\sin 2t$     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]