An interpolation scheme between fast and slow atom motion limits is presented based on the Mahanthappa-Baksi-Keldysh Green's function formalism for the time-dependent Newns-Anderson model. Its validity is examined for various limiting cases such as wide band limit, narrow band limit, slow atom-motion limit, and fast atom-motion limit. Various mathematically tractable models for time dependence and energy dependence for matrix elements appearing in the theory are employed. It is shown that the approximation is fairly good for most of the limits, but poor for the case in which an oscillatory behavior is observed in the charge fraction as a function of the atom velocity. It is also shown that the Landau-Zener tunneling theory must be modified when level crossing takes place and the atom motion is fast.