If a body is constantly accelerated from rest to a final velocity v, then the distance it goes in time t is the same as if it had travelled at constant velocity v/2. This fact, the Mean Velocity Law, was proved by Galileo on his way to proving the Law of Free Fall, a milestone in the evolution of modern physics. But the Mean Velocity Law itself was well known as far back as the Middle Ages. In this article, we compare Galileo�s mathematical approach to that of the medieval philosopher and mathematician, Nicole Oresme, and we also look at the scientific context�just what information the law gave�in each era, with some surprising results.
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