Which statement best resolves the arrow paradox by distinguishing between motion at an instant and motion over an interval?

Which statement best resolves the arrow paradox by distinguishing between motion at an instant and motion over an interval?

• A. The arrow paradox is resolved by time dilation.
• B. The resolution relies on discrete time steps.
• C. The resolution uses instantaneous velocity as a concept.
• D. The resolution distinguishes motion at an instant from motion over an interval.

Answer: (D)

Motion at an instant is described by instantaneous velocity—the rate at which position would change at that exact moment. Motion over an interval is about how far the position changes as time passes across a stretch of time, i.e., the total displacement or distance traveled, which comes from accumulating those tiny changes. The arrow can have a definite position at a single moment and still be moving, because the position is changing as time progresses. When you look at a single instant, you’re catching the slope of the position-time curve at that moment, not denying motion. Over a finite interval, that changing position adds up, so the arrow travels some distance even though each individual instant has its own position. This distinction is what resolves the paradox: separating the description of motion at an instant from the description of motion over an interval shows that there can be movement continuous in time even if you isolate each moment. Other ideas like time dilation or assuming motion only happens in discrete steps don’t capture how continuous change builds up over a span of time.

Motion at an instant is described by instantaneous velocity—the rate at which position would change at that exact moment. Motion over an interval is about how far the position changes as time passes across a stretch of time, i.e., the total displacement or distance traveled, which comes from accumulating those tiny changes.

The arrow can have a definite position at a single moment and still be moving, because the position is changing as time progresses. When you look at a single instant, you’re catching the slope of the position-time curve at that moment, not denying motion. Over a finite interval, that changing position adds up, so the arrow travels some distance even though each individual instant has its own position.

This distinction is what resolves the paradox: separating the description of motion at an instant from the description of motion over an interval shows that there can be movement continuous in time even if you isolate each moment. Other ideas like time dilation or assuming motion only happens in discrete steps don’t capture how continuous change builds up over a span of time.