By changing only the playback time of a motion sequence, an animator can achieve a variety of effects that can change our perception of an event. In some scenarios, it may be possible to consider physical properties of motion when retiming (eg. to preserve physical plausibility). However, existing retiming solutions can be quite time consuming when physical parameters are considered. This paper presents an interactive method for optimal motion retimings that takes into account physically based constraints and objective functions. We achieve fast performance through a precomputation phase where constraints are projected into the two-dimensional space of velocities and accelerations along the input motion path. Unlike previous approaches, our precomputation technique allows for rapid computation of plausible contact forces that result from retiming, and it also accomodates changing physical parameters. We demonstrate our approach by creating physically plausible results for changes in motion duration, manipulations of the gravity vector, and modifications of character limb masses.