Sensing the passage of time is important for countless daily tasks, yet time perception is easily influenced by perception, cognition, and emotion. Mechanistic accounts of time perception have traditionally regarded time perception as part of central cognition. Since proprioception, action execution, and sensorimotor contingencies also affect time perception, perception-action integration theories suggest motor processes are central to the experience of the passage of time. We investigated whether sensory information and motor activity may interactively affect the perception of the passage of time. Two prospective timing tasks involved timing a visual stimulus display conveying optical flow at increasing or decreasing velocity. While doing the timing tasks, participants were instructed to imagine themselves moving at increasing or decreasing speed, independently of the optical flow. In the direct-estimation task, the duration of the visual display was explicitly judged in seconds while in the motor-timing task, participants were asked to keep a constant pace of tapping. The direct-estimation task showed imagining accelerating movement resulted in relative overestimation of time, or time dilation, while decelerating movement elicited relative underestimation, or time compression. In the motor-timing task, imagined accelerating movement also accelerated tapping speed, replicating the time-dilation effect. The experiments show imagined movement affects time perception, suggesting a causal role of simulated motor activity. We argue that imagined movements and optical flow are integrated by temporal unfolding of sensorimotor contingencies. Consequently, as physical time is relative to spatial motion, so too is perception of time relative to imaginary motion.