| 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+cos2t, t⩾. 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}.
[5]
a.
Find the displacement of the particle when t = {t_1}
[2]
b.
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]
a.
s = \frac{\pi }{{12}} + \cos \frac{\pi }{6}\,\,\,\left( {s = \frac{\pi }{{12}} + \frac{{\sqrt 3 }}{2}(m)} \right) A1A1
[2 marks]
b.
Examiners report
[N/A]
a.
[N/A]
b.
