Mathematical Methods — Question 4

QCAA 2025, Paper 2 · 1 mark

Q4 · 2025 · Technology-activeSimple familiar1 mark

QUESTION 4

An object moves in a straight line such that its velocity (m s

^{-1}

) is given by

v(t)=t^2-e^{-t}

for

0\le t\le5

, where

t

represents time (s). Determine the time,

t

, when the acceleration of the object is

2

m s

^{-2}

(A)

0.768

(B)

1.157

(C)

3.865

(D)

4.135

ABCD

WORKED SOLUTION

1 mark

ANSWER

A —

0.768

Worked solution

Acceleration is

a(t)=v'(t)=2t+e^{-t}

. Solving

2t+e^{-t}=2

numerically gives

t\approx0.768

, so option A.

Selects option A.

[1 mark]

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