Velocity is the rate of change of displacement with time.This definition implies that
How should we choose the time interval appearing in Eq. (12)? Obviously, in the simple case in which the body is moving with constant velocity, we can make as large or small as we like, and it will not affect the value of . Suppose, however, that is constantly changing in time, as is generally the case. In this situation, must be kept sufficiently small that the body's velocity does not change appreciably between times and . If is made too large then formula (12) becomes invalid.
Suppose that we require a general expression for instantaneous velocity which
is valid irrespective of how rapidly or slowly the body's velocity changes in time.
We can achieve this goal by taking the limit of Eq. (12) as
zero. This ensures that no matter how rapidly varies with time, the velocity
of the body is always approximately constant in the interval to
The terms velocity and speed are often confused with one another. A velocity can be either positive or negative, depending on the direction of motion. The conventional definition of speed is that it is the magnitude of velocity (i.e., it is with the sign stripped off). It follows that a body can never possess a negative speed.