Moving dots

Calculus Level 3

A moving dot \(P\) departs from \(O\) at an initial speed of \(6\ \mbox{m/s}\) in the east direction, accelerating at \(2\ \mbox{m}\mbox{/s}^2\). Two seconds after \(P\)'s departure, dot \(Q\) departs from \(O\) to chase down \(P\) at a constant speed of \(k\ \mbox{m/s}\) in the east direction. What is the minimum speed, \(k\), required for \(Q\) to eventually catch up to \(P\)?

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