The physical optics approach and Lorentz transformations are combined to formulate scatter from a random rough surface in uniform motion. The perfectly conducting scatterer is excited by an elliptically polarized plane electromagnetic wave and the analysis ends in the velocity-dependent expressions for the scattering cross section per unit area, the depolarization factor and the radial tilt. The direction of motion is considered parallel as well as normal to the scatterer's mean plane. The combined effect of roughness and motion on scattering and depolarization is investigated through a numerical example. The calculations reveal that parallel motion modifies scatter through aberration while normal motion results in scatter amplification. The depolarization factor and/or radial tilt might be used for motion estimation.