This question was first addressed by Zeno of Elea around 400 BCE in his famous paradoxes of motion.
Aristotle, in his book Physics, pointed out that there was an adequate solution to this as per the usual solution by taking the sum of an infinite series. However he still said that this wasn't a full solution of the problem of motion in the small, and he offered a solution in terms of potentia & actuality.
The problem here is that taking the sum is merely a mathematical notion and not itself motion; it's an idealised picture. There is a difference between a physical continuum and a mathematical one.
That this problem is valid can be seen from the fact that motion in the small is given by quantum mechanics rather than classical mechanics, and quite incredibly we can view this motion in terms of potentia and actuality: the wave function - the potentia, and its measurement - the actuality. This is not to say that in the Greece of Antiquity they were doing Quantum Mechanics - far from it; what they did, by logical means, is realise that there is a problem in motion not adequately captured by our intuitive notions.
A similar problem was tackled by Al-Ghazali in a more wide-ranging way (he was addressing causality), for which he suggested occasionalism - that from moment to moment, in every place, the world in being created, decreated and recreated; and in this, he sees the hand of God.
In the early 20C the invention/discovery of QM showed to the surprise of physicists that physical motion isn't as simple as they had thought; the jury is out on its interpretation... The simplest motion is that of a single electron and here the wave function evolves in all directions, it doesn't have a classical path; this reminds me of an argument by Aristotle when he asked in which direction should a particle move in the void - his answer was in every direction, and because of this he concluded the void did not exist.