Mathematical Methods — Question 12

QCAA 2021, Paper 2 · 4 marks

Q12 · 2021 · Technology-activeSimple familiar4 marks

QUESTION 12 (4 marks)

The velocity function of an object in

\text{m s}^{-1}

is given by

v(t)=\cos\left(6t+\dfrac\pi2\right)+2

0\le t\le5

. Initially, the object is at the origin.

Determine the displacement function.

[2 marks]

What is the displacement of the object from the origin, in metres (m), after three seconds?

[2 marks]

WORKED SOLUTION

4 marks

ANSWER

s(t)=\dfrac16\sin(6t+\dfrac\pi2)+2t-\dfrac16

; b)

5.943

Worked solution

s(t)=\frac16\sin\left(6t+\frac\pi2\right)+2t+c.

Substituting

s(0)=0

gives

c=-\frac16

, hence

s(t)=\frac16\sin\left(6t+\frac\pi2\right)+2t-\frac16.

b) The marking guide evaluates

s(3)-s(0)=5.943

correctly determines the indefinite integral s(t)

[1 mark]

correctly determines the displacement function

[1 mark]

establishes an expression for the distance travelled

[1 mark]

determines distance travelled

[1 mark]

One QCAA sample method typeset for web; criterion wording is adapted from the official marking guide.

How many marks did you earn?

Compare your working with the guide above.