Thresholds for the detection of constant acceleration and deceleration of a discrete object moving along horizontal and vertical axes were studied. A staircase methodology was used to determine thresholds for three average velocities (0.7, 1.2, and 1.7 deg/sec). Thresholds, expressed as the proportion of velocity change, did not differ significantly among the average velocities; thus, a consistent Weber-like fraction is suggested by the data. Furthermore, there was an interaction between the axis of motion (horizontal or vertical) and the sign of the velocity change (acceleration or deceleration): accelerations were easier to detect along the vertical axis, decelerations along the horizontal axis.