A dynamically controlled retractable tether provides a mechanism by which a pet can be safely exercised on a bicycle or other vehicle. The pet avoids injury when running in front of the bicycle and stopping short, by having a detector detect the relative motion of the pet and the bicycle so as to automatically apply brakes to the bicycle prior to the pet being injured. Variations include a zone detection mechanism that detects a relative position of the pet relative to the bicycle, and uses a different set of braking parameters, depending on the zone in which the pet is located.