Answer
$$s(t)=t$$
Work Step by Step
Since
\begin{align*}
\mathbf{v}&=\frac{d}{d t}\left(x_{0}+t u_{1}\right) \mathbf{i}+\frac{d}{d t}\left(y_{0}+t u_{2}\right) \mathbf{j}+\frac{d}{d t}\left(z_{0}+t u_{3}\right) \mathbf{k}\\
&=u_{1} \mathbf{i}+u_{2} \mathbf{j}+u_{3} \mathbf{k}=\mathbf{u},\end{align*}
Then
\begin{align*}
s(t)&=\int_{0}^{t}|\mathbf{v}| d t\\
&=\int_{0}^{t}|\mathbf{u}| d \tau\\
&=\int_{0}^{t} 1 d \tau\\
&=t
\end{align*}
