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Date May Specimen paper Marks available 1 Reference code SPM.1.AHL.TZ0.7
Level Additional Higher Level Paper Paper 1 Time zone Time zone 0
Command term Write down Question number 7 Adapted from N/A

Question

A particle, A, moves so that its velocity ( ν  ms−1) at time t is given by ν = 2 sin  t , t ≥ 0.

The kinetic energy ( E ) of the particle A is measured in joules (J) and is given by E = 5 ν 2.

Write down an expression for E as a function of time.

[1]
a.

Hence find  d E d t .

[2]
b.

Hence or otherwise find the first time at which the kinetic energy is changing at a rate of 5 J s−1.

[2]
c.

Markscheme

E = 5 ( 2 sin t ) 2 ( = 20 si n 2 t )      A1

[1 mark]

a.

d E d t = 40 sin t cos t     (M1)A1

[2 marks]

b.

t = 0.126   (M1)A1

[2 marks]

c.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.

Syllabus sections

Topic 5—Calculus » AHL 5.9—Differentiating standard functions and derivative rules
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Topic 5—Calculus

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