Motion planning in the presence of time-dependent obstacles is studied. Many of the prior approaches to motion planning problems assume that the obstacles always exist in the environment, whether they are stationary of in motion. In this article, I consider the case that the environment contains obstacles whose existing periods are dependent on time (i.e., they can appear and disappear in the environment). This formulation allows us to model a variety of situations that can arise in application domains. A concept similar to that of visibility is used to solve the problem. An algorithm is presented to generate a motion in such a dynamic domain, its time-minimality is proved, and computation time is analyzed.