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Simulation has become an indispensable tool in the design and evaluation of mobile systems. By using mobility models that describe constituent movement, one can explore large systems, producing repeatable results for comparison between alternatives. In this paper, we show that a large class of mobility models - including all those in which nodal speed and distance or destination are chosen independently - have a transient period in which the average node speed decreases until converging to some long-term average. This speed decay provides an unsound basis for simulation studies that collect results averaged over time, complicating the experimental process. In this paper, we derive a general framework for describing this decay and apply it to a number of cases. Furthermore, this framework allows us to transform a given mobility model into a stationary one by initializing the simulation using the steady-state speed distribution and using the original speed distribution subsequently. This transformation completely eliminates the transient period and the decay in average node speed and, thus, provides sound models for the simulation of mobile systems.