  We revisit the linear search problem where a robot, initially placed at the
origin on an infinite line, tries to locate a stationary target placed at an
unknown position on the line. Unlike previous studies, in which the robot
travels along the line at a constant speed, we consider settings where the
robot's speed can depend on the direction of travel along the line, or on the
profile of the terrain, e.g. when the line is inclined, and the robot can
accelerate. Our objective is to design search algorithms that achieve good
competitive ratios for the time spent by the robot to complete its search
versus the time spent by an omniscient robot that knows the location of the
target. We consider several new robot mobility models in which the speed of the
robot depends on the terrain.These include 1) different constant speeds for
different directions, 2) speed with constant acceleration and/or variability
depending on whether a certain segment has already been searched, 3) speed
dependent on the incline of the terrain. We provide both upper and lower bounds
on the competitive ratios of search algorithms for these models, and in many
cases, we derive optimal algorithms for the search time.
