To intercept or avoid moving objects successfully, we must compensate for the sensorimotor delays associated with visual processing and motor movement. Although straightforward in the case of constant velocity motion, it is unclear how humans compensate for accelerations, as our visual system is relatively poor at detecting changes in velocity. Work on free-falling objects suggests that we are able to predict the effects of gravity, but this represents the most simple, limiting case in which acceleration is constant and motion linear. Here, we show that an internal model also predicts the effects of complex, varying accelerations when they result from lawful interactions with the environment. Participants timed their responses with the arrival of a ball rolling within a tube of various shapes. The pattern of errors indicates that participants were able to compensate for most of the effects of the ball acceleration (∼85%) within a relatively short practice (∼300 trials). Errors on catch trials in which the ball velocity was unexpectedly maintained constant further confirmed that participants were expecting the effect of acceleration induced by the shape of the tube. A similar effect was obtained when the visual scene was projected upside down, indicating that the mechanism of this prediction is flexible and not confined to ecologically valid interactions. These findings demonstrate that the brain is able to predict motion on the basis of prior experience of complex interactions between an object and its environment.