a) $v\left( {100} \right) = 0.16 \times 1000 - 0.016 \times 10000 = 0$

b) $a = 1.5 \times 0.16{t^{{\raise0.5ex\hbox{$\scriptstyle 1$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 2$}}}} - 0.032t$

$[{t^{{\raise0.5ex\hbox{$\scriptstyle 2$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 3$}}}} = 0.24/0.032 \to t = 56.25 \to $

${v_{max}} = 0.16 \times 421.875 - 0.016 \times 3164.0625]$

Maximum speed is $16.9{\text{ }}m{s^{ - 1}}$ (or $16\frac{7}{8}m{s^{ - 1}}$)

c) $s = 2/5 \times 0.16{t^{{\raise0.5ex\hbox{$\scriptstyle 5$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 2$}}}} - 0.016{t^3}/3$

Distance is $1070{\text{ }}m$

d) $\frac{1}{3}{t^{{\raise0.5ex\hbox{$\scriptstyle 5$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 2$}}}}(0.192 - 0.016\sqrt t ) = 0$

Value of $t$ is $144$