This paper addresses trajectory planning for a robot subject to dynamic constraints and moving in a dynamic workspace. A car-like robot M with bounded velocity and acceleration, moving in a dynamic two-dimensional workspace is considered. The solution proposed is an extension of the path-velocity decomposition which is a practical way to address trajectory planning in dynamic workspaces. However it presents a serious drawback: it cannot find a solution if a moving obstacle stops right on the computed path. Previous answers to this problem were to consider sets of candidate paths. The answer proposed in this paper makes use of the novel concept of adjacent paths (like adjacent lanes of the roadway). A set of adjacent paths, one of which leads M to its goal, is computed. Then, assuming that M is able to shift from one path to an adjacent one freely, the motion of M along and between these paths is determined so as to avoid the moving obstacles. The fact that it is possible to switch several times between two adjacent paths makes this approach more flexible and more powerful than one considering candidate paths.