Poor Bug, Will it ever succeed?

Classical Mechanics Level 5

An extremely stretchable rubber band of natural length \(\displaystyle L\) has its one end tied to a wall.
A bug peacefully rests at the outer end. Just when it seemed that everything was good, an evil-minded child starts pulling the outer end by a constant velocity \(\displaystyle v\). The bug immediately realizes the danger, and simultaneously starts crawling towards the other end at a speed \(\displaystyle u\) (relative to the band).

Will the bug ever reach the wall? If so, how long (in sec) would it take to reach it?

Answer \(\displaystyle 0\) if you think that the bug will never reach the wall.

Details and Assumptions:
\(\bullet\) \(\displaystyle L = 15 \text{ cm}\)
\(\bullet\) \(\displaystyle v = 3 \text{ cm/s}\)
\(\bullet\) \(\displaystyle u = 1 \text{ cm/s}\)


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