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Galileo didn't discover a mathematical relationship for distance traveled when an object is being accelerated, as the maths only became possible when Issac Newton invented the calculus (partly for the reason of finding such a relationship).

Galileo did discover objects accelerated at the same rate independent of mass in the gravitational field (a 10kg stone will hit the ground the same time as a 1kg stone if ignoring air) He suggested such experiments as dropping stones off the leaning tower of Pisa.

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Q: What relationship between distance traveled and time did Galileo discover for accelerating objects?
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