Expression have been derived that relate the stopping power and energy-loss straggling in a medium with internal motion for penetrating charged particles to the corresponding quantities applying to the equivalent medium at rest. These expressions have been based on a general binary-encounter picture and apply to nonrelativistic velocities and arbitrary mass ratios. Convenient expansions have been found in the limits of very high and very low projectile velocity. The results are applied to both nuclear and electronic stopping of charged particles. The capability of the scheme is tested upon the degenerate free-electron gas, for which accurate expansions at high and low projectile speed are known, with regard to both stopping and straggling. The scheme allows evaluation of shell corrections to stopping power and straggling of atomic and molecular gases beyond the range of validity of the leading terms in an expansion in inverse powers of electron velocity. A seeming disparity between high-speed straggling parameters calculated for the Fermi gas on the one hand, and an atomic target on the other hand, is attributed to different ground-state properties of the two systems in zero order. An essential difference is pointed out between the predictions of the dielectric theory and the present scheme with regard to the velocity dependence of energy-loss straggling in the low-speed limit.