In this paper we continue the study of the unified dynamics resulting from the theory of projected dynamical systems and evolutionary variational inequalities, initiated by Cojocaru, Daniele, and Nagurney. In the process we make explicit the interdependence between the two timeframes used in this new theory. The theoretical results presented here provide a natural context for studying applied problems in disciplines such as operations research, engineering, in particular, transportation science, as well as in economics and finance.