| MadSci Network: Physics |
Your question is similar to asking if it is ever possible to arrive at a final destination if you keep taking the remaining distance and going half way to the end.
But in your question the answer is that the distance between the slower and faster object gets smaller and the time it takes to cover that smaller distance also gets smaller. But when the time to overtake the slower object becomes zero the distance is also zero, and at that instant the faster object and the slower one are at the same distance from whatever point you are measuring. Then it is in front!!
If ds is the increment in distance and dt is the increment is time, we say that the velocity, v = ds / dt. And in this case the limit as ds and dt go to zero is still v, so the relative speed between the two objects does not change, and in the instant that ds is actually zero the faster object then goes to the front.
I hope this helps.
John Link
MadSci Scientist
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