Mathematical Methods — Question 5

QCAA 2020, Paper 2 · 1 mark

Q5 · 2020 · Technology-activeSimple familiar1 mark

QUESTION 5

An object moves in a straight line with a velocity

v

given by

v(t)=40(e^{-t}-e^{-2t})\;\mathrm{m\,s^{-1}},\quad t\ge0.

The object is at the origin initially. The displacement–time graph in the first 6 seconds is

ABCD

WORKED SOLUTION

1 mark

ANSWER

Worked solution

s(t)=\int40(e^{-t}-e^{-2t})dt=20-40e^{-t}+20e^{-2t}=20(1-e^{-t})^2

using

s(0)=0

. It starts at 0, increases and approaches 20, so C.

Selects option C.

[1 mark]

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