  We consider linear search for an escaping target whose speed and initial
position are unknown to the searcher. A searcher (an autonomous mobile agent)
is initially placed at the origin of the real line and can move with maximum
speed $1$ in either direction along the line. An oblivious mobile target that
is moving away from the origin with an unknown constant speed $v<1$ is
initially placed by an adversary on the infinite line at distance $d$ from the
origin in an unknown direction. We consider two cases, depending on whether $d$
is known or unknown. The main contribution of this paper is to prove a new
lower bound and give algorithms leading to new upper bounds for search in these
settings. This results in an optimal (up to lower order terms in the exponent)
competitive ratio in the case where $d$ is known and improved upper and lower
bounds for the case where $d$ is unknown. Our results solve an open problem
proposed in [Coleman et al., Proc. OPODIS 2022].
