Chasing B: A's Journey to Catch B at Distance d

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if particles A and B are at sepration of distance d and both start moving simultaniously with speed v and u , such that dir. of velocity of A always points towords the position of B and given that v>u , then to catch B , will A have to travell a distance of d irrespective of the direction of motion of b ? and why?
(given that they do nt move towards each other)
 
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You say irrespective of the direction of motion of B... but if B is moving towards A, then A will only cover a fraction of the distance d before it meets B coming toward it.

If B is moving away, then A will have to cover a distance greater than d to reach it.

The only way A will only have to cover distance d is if B isn't moving at all.
 
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