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Date May 2016 Marks available 2 Reference code 16M.2.hl.TZ1.3
Level HL only Paper 2 Time zone TZ1
Command term Find Question number 3 Adapted from N/A

Question

The displacement, s, in metres, of a particle t seconds after it passes through the origin is given by the expression s=ln(2et), t0.

Find an expression for the velocity, v, of the particle at time t.

[2]
a.

Find an expression for the acceleration, a, of the particle at time t.

[2]
b.

Find the acceleration of the particle at time t=0.

[1]
c.

Markscheme

vdsdt=et2et (=12et1 or 1+22et)     M1A1

[2 marks]

a.

a=d2sdt2=et(2et)et×et(2et)2 (=2et(2et)2)     M1A1

Note:     If simplified in part (a) award (M1)A1 for a=d2sdt2=2et(2et1)2.

Note:     Award M1A1 for a=et(2et)2(et)et(2et)1.

[2 marks]

b.

a=2 (ms2)     A1

[1 mark]

c.

Examiners report

Mostly well done. There were a few sign errors but most candidates were correctly applying the quotient or chain rules.

a.

Mostly well done. There were a few sign errors but most candidates were correctly applying the quotient or chain rules.

b.

Mostly well done. There were a few sign errors but most candidates were correctly applying the quotient or chain rules.

c.

Syllabus sections

Topic 6 - Core: Calculus » 6.6 » Kinematic problems involving displacement s, velocity v and acceleration a.
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