In previous research, direction detection thresholds have been measured and successfully modeled by exposing participants to sinusoidal acceleration profiles of different durations. In this paper, we present measurements that reveal differences in thresholds depending not only on the duration of the profile, but also on the actual time course of the acceleration. The measurements are further explained by a model based on a transfer function, which is able to predict direction detection thresholds for all types of acceleration profiles. In order to quantify a participant's ability to detect the direction of motion in the horizontal plane, a four-alternative forced-choice task was implemented. Three types of acceleration profiles (sinusoidal, trapezoidal and triangular) were tested for three different durations (1.5, 2.36 and 5.86 s). To the best of our knowledge, this is the first study which varies both quantities (profile and duration) in a systematic way within a single experiment. The lowest thresholds were found for trapezoidal profiles and the highest for triangular profiles. Simulations for frequencies lower than the ones actually measured predict a change from this behavior: Sinusoidal profiles are predicted to yield the highest thresholds at low frequencies. This qualitative prediction is only possible with a model that is able to predict thresholds for different types of acceleration profiles. Our modeling approach represents an important advancement, because it allows for a more general and accurate description of perceptual thresholds for simple and complex translational motions.