A problem on track runners

Consider the unit circle $C$ and a circular arc $A$ of length $\ell=|A| < 1$. It is shown that there exists $k=k(\ell) \in \mathbb{N}$, and a schedule for $k$ runners with $k$ distinct but constant speeds so that at any time $t \geq 0$, at least one of the $k$ runners is \emph{not} in $A$.