Mathematical Methods — Question 7

QCAA 2025, Paper 2 · 1 mark

Q7 · 2025 · Technology-activeSimple familiar1 mark

QUESTION 7

An object starts from rest at the origin with acceleration (m s

^{-2}

) given by

a(t)=16-t^2+t^3

for

t\ge0

, where

t

represents time (s). Determine the displacement from the origin of the object 1.5 seconds after it starts moving.

(A)

7.0

(B)

17.125

(C)

17.958

(D)

24.141

ABCD

WORKED SOLUTION

1 mark

ANSWER

C —

17.958

Worked solution

Integrating twice and using

v(0)=0

and

s(0)=0

v(t)=16t-\frac{t^3}{3}+\frac{t^4}{4},

s(t)=8t^2-\frac{t^4}{12}+\frac{t^5}{20}.

t=1.5

s\approx17.958

, so option C.

Selects option C.

[1 mark]

Worked explanation by QCE Vault; correct option verified against the QCAA answer key.