We present data on the human sensitivity to optic acceleration, i.e. temporal modulations of the speed and direction of moving objects. Modulation thresholds are measured as a function of modulation frequency and speed for different periodical velocity vector modulation functions using a localized target. Evidence is presented that human detection of velocity vector modulations is not directly based on the acceleration signal (the temporal derivative of the velocity vector modulation). Instead, modulation detection is accurately described by a two-stage model: a low-pass temporal filter transformation of the true velocity vector modulation followed by a variance detection stage. A functional description of the first stage is a second order low-pass temporal filter having a characteristic time constant of 40 msec. In effect, the temporal low-pass filter is an integration of the velocity vector modulation within a temporal window of 100-140 msec. A non-trivial link of this low-pass filter stage to the temporal characteristics of standard motion detection mechanisms will be discussed. Velocity vector modulations are detected in the second-stage, whenever the variance of the filtered velocity vector exceeds a certain threshold variance in either the speed or direction dimension. The threshold standard deviations for this variance detection stage are estimated to be 17% for speed modulations and 9% for motion direction modulations.