NCEA Calculus 2022 TWO(c - Solution & Explanation

Question

An object is travelling in a straight line. Its displacement, in metres, is given by the formula:

d(t) = \dfrac{t^2 - 6}{2t^3}

where

t > 0

,

t

is time in seconds.

Find the time(s) when the object is stationary.

*You must use calculus and show any derivatives that you need to find when solving this problem.*

Official Answer

d(t)=\dfrac{t^2-6}{2t^3}

v(t)=\dfrac{2t^3(2t)-(t^2-6)(6t^2)}{4t^6}

v(t)=\dfrac{36t^2-2t^4}{4t^6}

v(t)=\dfrac{18-t^2}{2t^4}

Stationary point when

v(t)=0

18-t^2=0

t=\sqrt{18}\;(=4.24)

Grading Criteria

Achievement (u)

Correct derivative.

Merit (r)

Correct solution with correct derivative.

Excellence T1

-

Excellence T2

-

Video Explanation

2022 NCEA L3 Calculus Exam Walkthrough by infinityplusone(starts at 31:54)

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2022 TWO(c)

Achievement (u)

Merit (r)

Excellence T1

Excellence T2