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