Perceptual thresholds for the detection of the direction of linear motion are important for motion simulation. There are situations in which a subject should not perceive the motion direction as, e.g., during repositioning of a simulator, but also opposite cases where a certain motion percept must intentionally be induced in the subject. The exact dependency of the perceptual thresholds on the time evolution of the presented motion profile is still an open question. Previous studies have found evidence for a sensitivity of the thresholds on the rate of change of acceleration, called jerk. In this study we investigate three motion profiles which differ in their jerk characteristics. We want to evaluate which profile can move people furthest in the horizontal plane in a given time without them noticing the direction. Our results suggest that a profile with a minimum peak jerk value should be chosen.