A smooth finite-time distributed control architecture is introduced and analyzed for the cooperative engagement problem. Using a time transformation method as well as Lyapunov stability theory, it is shown that the proposed architecture guarantees finite-time cooperative engagement in that the difference between the positions of each agent and a time-varying target, where this difference represents a dynamic equilibrium point, vanishes in a-priori given, user-defined finite time. In addition, this finite-time convergence is achieved without dependence on the initial conditions of agents and in the presence of unknown but bounded velocity of the target. Specifically, we first time transformed the proposed smooth finite-time distributed control architecture into an infinite-time (that is, stretched) interval. This time transformation method is then allowed to utilize tools from standard Lyapunov stability theory in which we analyze convergence properties of this architecture and boundedness of local control signals of each agent in this infinite-time interval. While this note focuses on a particular problem in the context of multiagent systems, the proposed time transformation method and the analysis procedure can be used for many other problems, where a-priori given, user-defined finite-time convergence is necessary with smooth control laws.