Introduction to integration — Question 169

Original QCE Vault practice · 5 marks

Q169 · Practice questionTechnology-freeComplex familiar5 marks

QUESTION 169 (5 marks)

The velocity–time graph of a particle is shown. The graph is linear between consecutive plotted points, and the initial position is

s(0)=7

Determine (a) the displacement from

t=0

t=6

, (b) the total distance travelled, and (c) the position at

t=6

WORKED SOLUTION

5 marks

ANSWER

(a)

10

m; (b)

14.5

m; (c)

17

Worked solution

Signed area from

0

4

6+6=12

. From

4

6

, the signed trapezoid area is

-2

, giving displacement

10

. The line crosses

v=0

t=4.5

; the absolute areas from

4

4.5

and

4.5

6

are

0.25

and

2.25

, so total distance is

12+0.25+2.25=14.5

. Final position is

7+10=17

Determines the signed area from

0

4

[1 mark]

Determines the signed area from

4

6

and hence displacement.

[1 mark]

Identifies the zero-velocity crossing.

[1 mark]

Determines total distance using absolute areas.

[1 mark]

Determines the final position.

[1 mark]

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

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