A hare runs a twomile race with a tortoise The tortoise has

A hare runs a two-mile race with a tortoise. The tortoise has a one-mile head start. Even though the hare runs ten times faster than the tortoise, it seems unable to catch up for the following reason: When the hare gets to the spot where the tortoise started, the tortoise is one-tenth of a mile farther on; when the hare gets to this one-and-one-tenth-mile point, the tortoise has moved on from it and is still ahead; and so on. Explain this seeming paradox.

Solution

This is famous Zeno \'s Paradox.

We can Use s=d/t

Greek philosophers of Zeno\'s day knew nothing about measuring speed. Using the above formula (from Galileo some thousand years after Zeno), you should be able to calculate precisely when and where the fleet-footed Achilles overtakes the lumbering Tortoise (assuming constant speeds).

There was never really any need to decompose the race into infinitely many, ever decreasing intervals. That was what we now call a dead end.

Hans Reichenbach has proposed that the paradox may arise from considering space and time as separate entities. In a theory like general relativity, which presumes a single space-time continuum, the paradox may be blocked

Peter Lynds has argued that all of Zeno\'s motion paradoxes are resolved by the conclusion that instants in time and instantaneous magnitudes do not physically exist^] Lynds argues that an object in relative motion cannot have an instantaneous or determined relative position (for if it did, it could not be in motion), and so cannot have its motion fractionally dissected as if it does, as is assumed by the paradoxes. For more about the inability to know both speed and location, see Heisenberg uncertainty principle.