Velocity

The velocity of a particle is defined, conceptually, as the rate at which the position of the object is changing. Mathematically, if we are given the position function (on a number line, for example) of an object with respect to time, $x(t)$, the velocity of the object is given by $$v(t) = \frac {\mathrm{d}x}{\mathrm{d}t} = x'(t).$$

Why do we not use the term speed instead of velocity? After all, aren't they the same thing $-$ they both describe how fast an object is moving.

No, actually. Velocity also describes the direction in which the object is moving. In other words, velocity is a vector, whereas speed is a scalar.

There a few different types of velocity one can use to describe an object. The first is instantaneous velocity. Instantaneous velocity as the limit of average velocity for short time intervals. In other words, it is the derivative of the position function at that particular instant.

Average velocity is defined as the displacement of an object over a certain elapsed time period divided by the elapsed time.

Exercise

Time rate of change of displacement is called velocity.

Unlike speed, velocity is a vector quantity, meaning it has magnitude as well as direction.

Velocity and speed have the same units and dimensions.

Total displacement divided by total time gives average velocity.

And instantaneous velocity is the velocity at a specific instant.

Note: For a body moving with uniform velocity, the instantaneous and the average velocities are equal.