Introduction to integration — Question 119

Original QCE Vault practice · 3 marks

Q119 · Practice questionTechnology-freeSimple familiar3 marks

QUESTION 119 (3 marks)

A particle moves along a straight line with velocity

v(t)=4-2t

and initial position

s(0)=3

. Determine

s(t)

and the first time after

t=0

at which the particle returns to its initial position.

WORKED SOLUTION

3 marks

ANSWER

s(t)=3+4t-t^2

and the particle returns at

t=4

Worked solution

Integrating gives

s(t)=4t-t^2+C

. Since

s(0)=3

C=3

. Setting

s(t)=3

gives

t(4-t)=0

, so the first positive return time is

4

Integrates the velocity correctly.

[1 mark]

Uses the initial position to determine the constant.

[1 mark]

Solves for the first positive return time.

[1 mark]

Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.

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