a
\(\begin{array}{l}
{\rm{Distance,}}\,{\rm{x = }}{\left( {t + 5} \right)^{ - 1}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( i \right)\\
Velocity,\,v = \frac{{dx}}{{dt}} = \frac{d}{{dt}}{\left( {t + 5} \right)^{ - 1}} = {\left( {t + 5} \right)^{ - 2}}\,\,\,\,\,\,....\left( {ii} \right)\\
Acceleration\\
\,\,\,\,\,\,\,\,\,\,\,\,a = \frac{{dv}}{{dt}} = \frac{d}{{dt}}\left[ { - {{\left( {t + 5} \right)}^{ - 2}}} \right] = 2{\left( {t + 5} \right)^{ - 3}}\,\,...\left( {iii} \right)\\
From\,equation\,\left( {ii} \right),\,we\,get\,\\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{v^{3/2}} =  - {\left( {t + 5} \right)^{ - 3}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( {iv} \right)\\
Substituting\,this\,in\,equation\,\left( {iii} \right)\,we\,get\\
Acceleration,\,a =  - 2{v^{3/2}}\,\,or\,\,a \propto {\left( {velocity} \right)^{3/2}}\\
From\,equation\,\left( i \right),\,we\,get\\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{x^3} = {\left( {t + 5} \right)^{ - 3}}\\
Substituting\,this\,in\,equation\,\left( {iii} \right),\,we\,get\\
Acceleration,\,\,\,\,\,\,\,\,\,\,\,a = 2{x^3}\,\,or\,\,a \propto {\left( {{\rm{distance}}} \right)^3}\\
Hence\,option\left( a \right)\,is\,correct.
\end{array}\)