Find \(t\) when \(v=4\)
\begin{align}t & \propto \frac{1}{v^2}\\
So \quad t & =k (\frac{1}{v^2}) \\
By \; substitution \quad 11 & =k(\frac{1}{2^2})\\
k & =44\\
\therefore \quad t & = 44(\frac{1}{v^2})\\
And \; when \; v & =4\\
t & = 44(\frac{1}{4^2})\\
\therefore \quad t & =\frac{11}{4}
\end{align}
Find \(v\) when \(t=9\)
\begin{align}t & \propto \frac{1}{v^2}\\
So \quad t & =k (\frac{1}{v^2}) \\
By \; substitution \quad 11 & =k(\frac{1}{2^2})\\
k & =44\\
\therefore \quad t & = 44(\frac{1}{v^2})\\
And \; when \; t=9\\
9 & = 44(\frac{1}{v^2})\\
v^2 & =\frac{44}{9}\\
\therefore \quad v & = \pm \sqrt{\frac{44}{9}}
\end{align}