In Galileo's time, the technology was not developed enough to verify whether an object was moving at a uniform speed by directly measuring the instantaneous speed. However, Galileo concluded by applying mathematical reasoning that the displacement of an object with uniform motion and zero initial velocity is proportional to the square of the time used, that is, S = at 2. Therefore, it can be verified whether an object is moving at a constant speed by measuring the time it takes for it to pass through different displacements.

How did Galileo deduce S = 1/2gt 2? His idea is roughly as follows: first, get s= Vt from the average speed. He deduced that the average speed of uniform variable speed motion with zero initial speed and V terminal speed is v=(v0+v terminal) /2, and then applied this relationship to get s= v terminal t/2. Then apply g=(v -v0)/t to eliminate v from the above formula, and derive S = gt 2/2, that is, S = 1/2gt 2.