a
\(\begin{array}{l}
Give:\,x = 9{t^2} - {t^3}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( i \right)\\
Speed\,v = \frac{{dx}}{{dt}} = \frac{d}{{dt}}(9{t^2} - {t^3}) = 18t - 3{t^2}.\\
For\,{\rm{maximum}}\,speed,\,\frac{{dv}}{{dt}} = 0\,\, \Rightarrow \,18 - 6t = 0\\
\therefore \,\,t = 3\,\,\,\,s.\\
\therefore {x_{\max }} = 81\,\,m - 27\,\,m = 54\,m.\,\left( {From\,x\, = \,9{t^2} - {t^3}} \right)
\end{array}\)