This paper addresses motion planning for a car-like robot moving in a changing planar workspace, i.e. with moving obstacles. First, this motion planning problem is formulated in the `state-time space' framework. The state-time space of a robot is its state space plus the time dimension. In this framework part of the constraints at hand are translated into static forbidden regions of state-time space, and a trajectory maps to a state-time curve which must respect the remaining constraints. Then an approximate solution to the problem is presented.