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Using the equation of motion s = ut + (1/2)at^2, where s is the distance, u is the initial velocity, a is acceleration, and t is time, we can find the final speed. We know that initial velocity, u, is 0 as the stone is dropped from rest. The acceleration, a, would be due to gravity (-9.8 m/s^2). Rearrange the equation to find final speed, v: v = at. Plug in the values: v = 9.8 m/s^2 * 6s = 58.8 m/s. So, the final speed of the stone when it hits the bottom of the well is 58.8 m/s.

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