This paper is concerned with obtaining closed-form exact solution for the 2-D canonical problem of the reflected field from a moving planar discontinuity of a dielectric–magnetic medium that is excited by an impulsive line current. The spectral theory of transient (STT) that originally deals with nondispersive frequency-domain plane-wave spectra is used in this paper for addressing a time-variant scattering problem. The scattering from a moving object yields dispersive and anisotropic PW spectra. Nevertheless, we demonstrate that the STT is capable of dealing with these types of spectra and obtain the desired exact time-dependent solutions. The unique wave phenomena that are associated with the medium and scatterer velocity are explored.