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Date May 2017 Marks available 1 Reference code 17M.2.SL.TZ1.S_7
Level Standard Level Paper Paper 2 Time zone Time zone 1
Command term Write down Question number S_7 Adapted from N/A

Question

A particle P moves along a straight line. Its velocity vP ms1 after t seconds is given by vP=tsin(π2t), for 0t8. The following diagram shows the graph of vP.

M17/5/MATME/SP2/ENG/TZ1/07

Write down the first value of t at which P changes direction.

[1]
a.i.

Find the total distance travelled by P, for 0t8.

[2]
a.ii.

A second particle Q also moves along a straight line. Its velocity, vQ ms1 after t seconds is given by vQ=t for 0t8. After k seconds Q has travelled the same total distance as P.

Find k.

[4]
b.

Markscheme

t=2     A1     N1

[1 mark]

a.i.

substitution of limits or function into formula or correct sum     (A1)

eg80|v|dt, |vQ|dt, 20vdt42vdt+64vdt86vdt

9.64782

distance =9.65 (metres)     A1     N2

[2 marks]

a.ii.

correct approach     (A1)

egs=t, k0tdt, k0|vQ|dt

correct integration     (A1)

egt=23t32+c, [23x32]k0, 23k32

equating their expression to the distance travelled by their P     (M1)

eg23k32=9.65, k0tdt=9.65

5.93855

5.94 (seconds)     A1     N3

[4 marks]

b.

Examiners report

[N/A]
a.i.
[N/A]
a.ii.
[N/A]
b.

Syllabus sections

Topic 5—Calculus » AHL 5.13—Kinematic problems
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