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1.1 Formal Definition of Velocity

The speed of an object is the magnitude or absolute value of its velocity. Consider an object moving along a straight line. Suppose we know its position p(t) as a function of time t in some time range.

Its average velocity between any two times, t1 and t2, is given by

Average velocity =                                         

Its velocity (or instantaneous velocity) at time t, v(t), is the limit of its average velocity over a sequence of time intervals starting at t, whose lengths, Dt, converge to 0.

Velocity =

Given the position function p, the process of finding v(t) is called differentiation. Given v, finding p(t) is called integration.