$$\require{cancel}$$

# Exercise 10.1.1

\begin{equation*} \begin{aligned} d = a\ell \quad \Longrightarrow \quad \ell = \frac{d}{a} \end{aligned} \end{equation*}
Substituting for $$\ell$$ in $$v = \dot a \ell$$, we get
\begin{equation*} \begin{aligned} v = \frac{\dot a}{a}d \end{aligned} \end{equation*}
Now substituting in $$\dot a/a = H$$, we get
\begin{equation*} \begin{aligned} v = H d \end{aligned} \end{equation*}