The utility of projection operator formalisms for describing the dynamics of many-body systems is studied, and the compatibility of these formalisms with certain approximation schemes is evaluated in the light of known behavior of such systems. For simplicity the investigation is limited to the study of Brownian motion. Specifically, a memory kernel formalism and a kinetic equation formalism are compared for the calculation of the time evolution of the momentum autocorrelation function. Both perturbation expansions and averaged propagator approximations are investigated. The results from these studies suggest that the long-time behavior of the momentum autocorrelation function is sensitive to the long-range nature of the interparticle potential.