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Date	November 2018	Marks available	2	Reference code	18N.2.SL.TZ0.S_4
Level	Standard Level	Paper	Paper 2	Time zone	Time zone 0
Command term	Find	Question number	S_4	Adapted from	N/A

Question

A particle moves along a straight line so that its velocity, $v$ m s⁻¹, after $t$ seconds is given by $v\left( t \right) = {1.4^t} - 2.7$ , for 0 ≤ $t$ ≤ 5.

Find when the particle is at rest.

[2]

Find the acceleration of the particle when $t = 2$ .

[2]

Find the total distance travelled by the particle.

[3]

Markscheme

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

valid approach (M1)

eg $v\left( t \right) = 0$ , sketch of graph

2.95195

$t = {\text{lo}}{{\text{g}}_{1.4}}2.7$ (exact), $t = 2.95$ (s) A1 N2

[2 marks]

valid approach (M1)

eg $a\left( t \right) = v'\left( t \right)$ , $v'\left( 2 \right)$

0.659485

$a\left( 2 \right)$ = 1.96 ln 1.4 (exact), $a\left( 2 \right)$ = 0.659 (m s⁻²) A1 N2

[2 marks]

correct approach (A1)

eg $\int_0^5 {\left| {v\left( t \right)} \right|} \,{\text{d}}t$ , $\int_0^{2.95} {\left( { - v\left( t \right)} \right)} \,{\text{d}}t + \int_{295}^5 {v\left( t \right)} \,{\text{d}}t$

5.3479

distance = 5.35 (m) A2 N3

[3 marks]

Examiners report

[N/A]

Syllabus sections

Topic 5—Calculus » AHL 5.13—Kinematic problems

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Find the time taken for the snail to reach the point $(10, 2)$ .
19M.2.SL.TZ2.S_8e.i:
Given that particles A and B start at the same point, find the displacement function ${s_{\text{B}}}$ for particle B.
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Find the value of $t$ when particle A first changes direction.
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22M.1.AHL.TZ2.17b.ii:
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21N.1.AHL.TZ0.8b:
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22M.1.AHL.TZ2.17a:
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19M.1.SL.TZ1.S_7b:
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18M.2.SL.TZ2.S_9e:
Find the total distance travelled by P.
18M.2.SL.TZ2.S_9a:
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17M.2.AHL.TZ1.H_11c:
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17N.2.SL.TZ0.S_9a:
Write down the values of $t$ when $a = 0$ .
18M.2.SL.TZ2.S_9b:
Find the maximum speed of P.
18M.2.AHL.TZ2.H_7b.ii:
Find the value of the acceleration of P at time t₁.
17M.2.SL.TZ1.S_7a.ii:
Find the total distance travelled by P, for $0 \leqslant t \leqslant 8$ .
17M.2.SL.TZ2.S_7:
Note: In this question, distance is in metres and time is in seconds.

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Find the greatest speed of $P$ in the interval $0 \leq t \leq 6$ .
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Find the total distance travelled by the particle.
17N.2.SL.TZ0.S_9c:
Find an expression for the velocity of P at time $t$ .
18M.2.SL.TZ2.S_9c:
Write down the number of times that the acceleration of P is 0 m s⁻² .
16N.2.SL.TZ0.S_9c:
(i) Find the value of $q$ .

(ii) Hence, find the speed of P when $t = q$ .
19M.2.AHL.TZ2.H_6:
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21M.2.AHL.TZ1.6d:
Find the magnitude of the velocity of the ice-skater when $t = 2$ .
21M.2.AHL.TZ1.6e:
At a point $P$ , the ice-skater is skating parallel to the $y$ -axis for the first time.

Find $OP$ .
21M.2.AHL.TZ1.6c:
Find the value of $a$ and the value of $b$ .
19M.1.SL.TZ1.S_7a:
Find the value of $s\left( 4 \right) - s\left( 2 \right)$ .
17N.1.AHL.TZ0.H_5:
A particle moves in a straight line such that at time $t$ seconds $(t \geqslant 0)$ , its velocity $v$ , in ${\text{m}}{{\text{s}}^{ - 1}}$ , is given by $v = 10t{{\text{e}}^{ - 2t}}$ . Find the exact distance travelled by the particle in the first half-second.
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Find his velocity when $t = 15$ .
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Find an expression for the acceleration of P at time t.
19M.2.SL.TZ2.S_8e.ii:
Find the other value of $t$ when particles A and B meet.
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Find the times when $P$ is at instantaneous rest.
21M.2.AHL.TZ2.6e:
Find the total distance travelled by $P$ in the interval $0 \leq t \leq 4$ .
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Find the displacement of the particle when $t = {t_1}$
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Find the velocity vector at time $t$ .
EXN.2.AHL.TZ0.7b.ii:
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Find an expression for the acceleration of the ball at time $t$ .
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EXN.2.AHL.TZ0.7c.ii:
Find the value of $t$ at the instant the string breaks.
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21N.1.AHL.TZ0.8a.ii:
Interpret this point in the given context.

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