Observers are often required to adjust actions with objects that change their speed. However, no evidence for a direct sense of acceleration has been found so far. Instead, observers seem to detect changes in velocity within a temporal window when confronted with motion in the frontal plane (2D motion). Furthermore, recent studies suggest that motion-in-depth is detected by tracking changes of position in depth. Therefore, in order to sense acceleration in depth a kind of second-order computation would have to be carried out by the visual system. In two experiments, we show that observers misperceive acceleration of head-on approaches at least within the ranges we used [600-800 ms] resulting in an overestimation of arrival time. Regardless of the viewing condition (only monocular or monocular and binocular), the response pattern conformed to a constant velocity strategy. However, when binocular information was available, overestimation was highly reduced.