Introduction to integration — Question 39

Original QCE Vault practice · 4 marks

Q39 · Practice questionTechnology-freeComplex familiar4 marks

QUESTION 39 (4 marks)

A particle moves along a straight line with velocity

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

for

0\le t\le4

. Determine the total distance travelled.

WORKED SOLUTION

4 marks

ANSWER

4

units.

Worked solution

v(t)=(t-1)(t-3)

changes sign at

t=1,3

. An antiderivative is

F(t)=t^3/3-2t^2+3t

. The distances on

[0,1]

[1,3]

and

[3,4]

are each

4/3

, so the total distance is

4

Finds the zeros

t=1,3

and identifies the sign changes.

[1 mark]

Finds a suitable antiderivative.

[1 mark]

Calculates the distance over the three intervals.

[1 mark]

Determines total distance

4

[1 mark]

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

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