  Consider search on an infinite line involving an autonomous robot starting at
the origin of the line and an oblivious moving target at initial distance $d
\geq 1$ from it. The robot can change direction and move anywhere on the line
with constant maximum speed $1$ while the target is also moving on the line
with constant speed $v>0$ but is unable to change its speed or direction. The
goal is for the robot to catch up to the target in as little time as possible.
  The classic case where $v=0$ and the target's initial distance $d$ is unknown
to the robot is the well-studied ``cow-path problem''. Alpert and Gal gave an
optimal algorithm for the case where a target with unknown initial distance $d$
is moving away from the robot with a known speed $v<1$. In this paper we design
and analyze search algorithms for the remaining possible knowledge situations,
namely, when $d$ and $v$ are known, when $v$ is known but $d$ is unknown, when
$d$ is known but $v$ is unknown, and when both $v$ and $d$ are unknown.
Furthermore, for each of these knowledge models we consider separately the case
where the target is moving away from the origin and the case where it is moving
toward the origin. We design algorithms and analyze competitive ratios for all
eight cases above. The resulting competitive ratios are shown to be optimal
when the target is moving towards the origin as well as when $v$ is known and
the target is moving away from the origin.
