The normal view is that the object occupies each and every position on its path until it reaches its destination. But the number of possible positions between any two points is infinite. Let's say no, or else my crackpot theory falls apart. Under my crackpot theory, objects actually disappear and then reappear along their path. They only seem to move because it happens so quickly.
Slow objects pop into existence slightly ahead of their last position.
A fast-traveling clock, for example, would have less time in existence to tick. If you could see it whizzing past you, it would appear slow. Obviously all of this popping in and out of existence would have to be happening so fast we can't notice or measure it. It might seem impossible that objects pop in and out of existence. But physicists know that's exactly what happens in the super-tiny quantum world.