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Date May 2017 Marks available 5 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 \({t_2}\).

[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.

Syllabus sections

Topic 6 - Core: Calculus » 6.6
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