High image quality video surveillance systems have proliferated making it more common to have collision-related video footage that is suitable for detailed analysis. This analysis begins by using variety of methods to reconstruct a series of positions for the vehicle. If the frame rate is known or can be estimated, then the average travel speed between each of those vehicle positions can be found. Unfortunately with video surveillance systems, the frame rates are typically low and the vehicle may be hidden from view for multiple frames. As a result there are often relatively large time steps between known vehicle positions and the average speed between known positions becomes less useful.The method outlined here determines the instantaneous speed and acceleration time history of the vehicle that was required for it to arrive at the known positions, at the known times. The position time history is reviewed and approximately broken in phases of constant acceleration (whether negative, positive or equal to zero). A Monte Carlo simulation is run using randomly chosen accelerations and durations for each phase. The start speed is estimated from the video and also used as a random variable in the Monte Carlo analysis. The resulting piecewise continuous model of the driver’s acceleration behavior is used to predict the vehicle’s position time history, which is compared with a least squares fit against the known positions to find the best overall match with the surveillance video.A series of staged tests done with known speed and acceleration time histories was conducted. The resulting video footage taken with a consumer surveillance system was analyzed using this method and the results were compared with the known values.