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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 2 t ,   t 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 2 t

d s d t = 1 2 sin 2 t      M1A1

= 0      M1

sin 2 t = 1 2

t 1 = π 12 ( s ) ,   t 2 = 5 π 12 ( s )      A1A1

 

Note:     Award A0A0 if answers are given in degrees.

 

[5 marks]

a.

s = π 12 + cos π 6 ( s = π 12 + 3 2 ( m ) )      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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Topic 5—Calculus

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