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.