We show a formal result of the longitudinal force acting on a moving potent
ial. The potential can be velocity dependent, which appears in various inte
resting physical systems, such as electrons in the presence of a magnetic f
lux line, or phonons scattering off a moving vortex. By using the phase-shi
ft analysis, we are able to show the equivalence between the adiabatic pert
urbation theory and the kinetic theory for the longitudinal force in the di
lute gas limit. [S0163-1829(98)01446-5].