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Date	May 2017	Marks available	2	Reference code	17M.1.AHL.TZ2.H_4
Level	Additional Higher Level	Paper	Paper 1	Time zone	Time zone 2
Command term	Find	Question number	H_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 ${t_2}$ .

[5]

a.

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

[2]

b.

Markscheme

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

$s = t + \cos 2t$

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

Syllabus sections

Topic 5—Calculus » AHL 5.13—Kinematic problems

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