#### Answer

$$1$$

#### Work Step by Step

Since speed is given by
\begin{align*}
\frac{d s}{d t}&=\sqrt{x^{\prime}(t)^{2}+y^{\prime}(t)^{2}}\\
&=\sqrt{ 4t^2+e^{2t} }
\end{align*}
Then
\begin{align*}
\frac{d s}{d t}\bigg|_{t=0} &=\sqrt{ 4t^2+e^{2t} } \\
&=1
\end{align*}