NCEA Calculus 2019 THREE(d - Solution & Explanation

Question

The velocity of an object is modelled by the function

v = 2e^t + 8e^{-t}

, for

t \ge 0

where

v

is the velocity of the object, in m s

^{-1}

and

t

is the time in seconds since the start of the object’s motion.

Find the time when the acceleration of the object is 0.

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

Official Answer

a(t)=2e^{t}-8e^{-t}

a(t)=0

\Rightarrow 2e^{t}-8e^{-t}=0

2e^{t}=8e^{-t}

e^{2t}=4

2t=\ln 4

t=\frac{1}{2}\ln 4\;(=\ln 2=0.693)

Grading Criteria

Achievement (u)

Correct derivative.

Merit (r)

Correct solution with correct derivative.

Excellence T1

-

Excellence T2

-

Video Explanation

NCEA Level 3 Calculus Differentiation 2019 NZQA Exam - Worked Answers by infinityplusone(starts at 54:37)

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2019 THREE(d)

Achievement (u)

Merit (r)

Excellence T1

Excellence T2