A particle of unit mass undergoes one di | vedclass

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Question

$\begin{array}{l}
Accordind\,to\,question,\,velocity\,of\,unit\,\
mass\,{m{varies}}\,as\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,v\left( x ight) = \b

Vedclass · Accepted Answer

$-2n$${\beta ^2}{X^{ - 4n - 1}}$

Vedclass · Answer

$\begin{array}{l}
Accordind\,to\,question,\,velocity\,of\,unit\,\
mass\,{m{varies}}\,as\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,v\left( x ight) = \beta {x^{ - 2n}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( i ight)\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{{dv}}{{dx}} =  - 2n\beta {x^{ - 2n - 1}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( {ii} ight)\
Acceleration\,of\,the\,particle\,is\,give\,by\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,a = \frac{{dv}}{{dt}} = \frac{{dv}}{{dx}} 	imes \frac{{dx}}{{dt}} = \frac{{dv}}{{dx}} 	imes v\
{m{Using}}\,equation\,\left( i ight)\,and\,\left( {ii} ight),\,we\,get\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,a = \left( { - 2n\beta {x^{ - 2n - 1}}} ight) 	imes \left( {\beta {x^{ - 2n}}} ight) =  - 2n{\beta ^2}{x^{ - 4n - 1}}
\end{array}$

A particle of unit mass undergoes one dimensional motion such that its velocity varies according to $ v(x)= \beta {x^{ - 2n}}$, where $\beta$ and $n$ are constants and $x$ is the position of the particle. The acceleration of the particle as a function of $x$, is given by

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