2022HSCShort answer

Q12 (c) (ii)

2 marks

Question

Hence, or otherwise, find $x$ as a function of $v$ .

Try the question before revealing the answer.

Solution

Criteria	Marks
Provides correct solution	2
Separates the variables from the DE in part (i), or equivalent merit	1

Sample answer:

\frac{dv}{dx}=-(1+3v),\qquad \int\frac{dv}{1+3v}=-\int dx

\frac13\ln|1+3v|=-x+c

When $x=0$ , $v=u$ :
$\frac13\ln|1+u|=c$

x=\frac13\ln|1+3u|-\frac13\ln|1+3v| =\frac13\ln\left(\frac{1+3u}{1+3v}\right)

Since $1+3v>0$ and $1+3u>0$ .

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Syllabus alignment

Mechanics

Resisted motionDerive and solve motion models with resistance on horizontal and vertical paths, including terminal velocity.

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