Interaction of electromagnetic, acoustic, and even gravitational waves with accelerating bodies forms a class of nonstationary time-variant processes. Scattered waves contain intrinsic signatures of motion, which manifest in a broad range of phenomena, including Sagnac interference, and both Doppler and micro-Doppler frequency shifts. Although general relativity is often required to account for motion, instantaneous rest frame approaches are frequently used to describe interactions with slowly accelerating objects. We investigate theoretically and experimentally an interaction regime that is neither relativistic nor adiabatic. The test model considers an accelerating scatterer with a long-lasting relaxation memory. The slow decay rates violate the instantaneous reaction assumption of quasistationarity, introducing non-Markovian contributions to the scattering process. Memory signatures in scattering from a rotating dipole are studied theoretically, showing symmetry breaking of micro-Doppler combs. A quasistationary numeric analysis of scattering in the short-memory limit is proposed and validated experimentally with an example of electromagnetic pulses interacting with a rotating wire.