The relation between time and motion is that of conceptual inseparability: motion only occurs through time, and time only passes in a universe in which objects move. In physics, motion refers to the change of position of an object through time. Time is a measure of change between two states; in the material universe, change in matter occurs through motion.
Motion conceptually requires time, as well as space. A state of motion is defined by the velocity of the object, that is, by its speed and direction. Speed is measured by the time an object takes to go over a certain distance. Hence, motion cannot occur in a timeless universe.
Similarly, time requires two different states in order to be measured. In a completely motionless universe, there would not make sense to say that a second, a year or a quadrillion centuries have passed, because there are no reference points (two distinct states of motion of the same object) to measure time.
Just the perception of motion does not imply that time does exist. A recent hypothesis postulates a "block universe" in which past, present and future are individual points. In this universe, time does not pass: all the events are one-dimensional points. Humans would perceive this universe as if time was passing, but it would only be an illusion. This is why the relation between time and motion is that of conceptual inseparability, rather than physical inseparability.