Please prove that the displacement difference of an object moving in a straight line with uniform speed change is a constant value in any two consecutive equal time periods. Let the acceleration be a and the time periods be continuous and equal If t is t and the displacement difference is Δ x, then Δ x = the square of a * t

Suppose: the velocity of the object at a certain time is vo
Then the displacement X1 = VOT + 1 / 2at & # 178 in t time;
In the later time t, the displacement x2 = (VO + at) t + 1 / 2at & # 178;
Displacement difference Δ x = x2-x1 = at & # 178;

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