There is an ancient puzzle about motion in Plato at Parmenides 155e-157b which has been the subject of scholarship by Richard Sorabji and more recently, Nico Strobach.1 The puzzle, as Plato gives it, can be roughly summarized as follows: At every time, a given object must either be in motion or at rest; there is no third possibility. Also, an object can never be simultaneously both in motion and at rest. The only way for an object to be both in motion and at rest is for it to be in motion and at rest at different times. But how does a thing come to be in motion at one time and at rest at another? It cannot switch at a time when it is in motion. Nor can it switch at a time when it is at rest. This would seem to exhaust the possibilities for the times when the switch could occur. But a thing cannot change without changing.
Bowin, John, "Plato and Aristotle on the Instant of Change - A Dilemma" (2008). The Society for Ancient Greek Philosophy Newsletter. 382.