# 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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