I have read about Zeno's arrow paradox that tells us there is no motion of the arrow at a particular instant of its flight. It can be inferred that there can be no velocity at any instant. Moreover we cannot calculate velocity at any instant in the real world (of course it can be done by using calculus) but how can this be possible? What is the intuition behind this concept?
Answer
At a "frozen" instant of time, the arrow may not be moving - but this is a tautology, since movement is something that requires time. However, even in that frozen instant the arrow does have a velocity (instantaneous velocity, if you will). Imagine that time is a series of huge number of discrete frames (or instead imagine that it is continuous, and that we are taking finer and finer discrete approximations). The position of the arrow jumps to the right from frame to frame. How does the arrow "know" how far to travel from one frame to the next? If the only piece of information "stored" in one frame were its position, then the arrow wouldn't be able to determine this! The necessary information, which is the instantaneous velocity of the arrow, must be as much a part of this frozen frame as all the information related to the arrow's position.
More formally, one says that the configuration space of a physical system, which is the set of all information needed to predict its future (and thus all the information associated with a point in time) includes not only the list of positions of all objects, but also their velocities.
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