Introduction to integration — Question 89

Original QCE Vault practice · 5 marks

Q89 · Practice questionTechnology-freeComplex familiar5 marks

QUESTION 89 (5 marks)

A particle has acceleration

a(t)=6t-12

, velocity

v(0)=9

and position

s(0)=4

. Determine the total distance travelled for

0\le t\le4

WORKED SOLUTION

5 marks

ANSWER

12

units.

Worked solution

Integrating gives

v(t)=3t^2-12t+9=3(t-1)(t-3)

and

s(t)=t^3-6t^2+9t+4

. The direction changes at

t=1

and

t=3

. Positions are

s(0)=4

s(1)=8

s(3)=4

s(4)=8

, so total distance is

4+4+4=12

Determines

v(t)

using the initial velocity.

[1 mark]

Finds direction changes at

t=1,3

[1 mark]

Determines

s(t)

using the initial position.

[1 mark]

Evaluates the positions at the relevant times.

[1 mark]

Adds the absolute changes to obtain

12

units.

[1 mark]

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

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