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Date	November 2015	Marks available	3	Reference code	15N.2.sl.TZ0.6
Level	SL only	Paper	2	Time zone	TZ0
Command term	Find	Question number	6	Adapted from	N/A

Question

The velocity $v{\text{ m}}{{\text{s}}^{ - 1}}$ of a particle after $t$ seconds is given by

$v(t) = {(0.3t + 0.1)^t} - 4$ , for $0 \le t \le 5$

The following diagram shows the graph of $v$ .

Find the value of $t$ when the particle is at rest.

[3]

Find the value of $t$ when the acceleration of the particle is $0$ .

[3]

Markscheme

recognizing particle at rest when $v = 0$ (M1)

eg $\;\;\;{(0.3t + 0.1)^t} - 4 = 0$ , $x$ -intercept on graph of $v$

$t = 4.27631$

$t = 4.28{\text{ }} {\text{ (seconds)}}$ A2 N3

[3 marks]

valid approach to find $t$ when $a$ is $0$ (M1)

eg $\;\;\;v'(t) = 0$ , $v$ minimum

$t = 1.19236$

$t = 1.19{\text{ }}{\text{ (seconds)}}$ A2 N3

[3 marks]

Total [6 marks]

Examiners report

[N/A]

Syllabus sections

Topic 6 - Calculus » 6.6 » Kinematic problems involving displacement

$s$ , velocity

$v$ and acceleration

$a$ .

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