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|| Galileo’s marbles. Galileo used marbles rolling down inclined planes to deduce some basic properties of constant accelerated motion. In particular, he measured the distance a marble rolled during specific time periods. For example, suppose a marble starts from rest and begins rolling down an inclined plane with constant acceleration a. After 1 s, you find that it moved a distance x. (a) In terms of x, now for does it move in the next 1 s time per oc—that is, in the time between 1 s and 2 s? (b) How far does it move in the next second of the motion? (c) How far does it move in the nth second of the motion?
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