Answer
The speed of motorist is 30 mph and the officer should believe the motorist as the speed limit is 35 miles.
Work Step by Step
Substitute $45$ for $L$ in the provided formula and calculate $v$.
$\begin{align}
& v=2\sqrt{5L} \\
& =2\sqrt{5\times 45}
\end{align}$
Write $45$ into its prime factors and take the square root.
$\begin{align}
& v=2\sqrt{5\times 5\times {{3}^{2}}} \\
& =2\times 5\times 3 \\
& =30
\end{align}$
Thus, the speed of motorist was $30\text{ mph}$.
Since it is less than $35\text{ mph}$, she was not speeding.
