Velocity is the change in displacement of an object over a change in time (a time interval or two points in time). The term "velocity" is often interchanged with the term "average velocity." Instantaneous velocity refers to the displacement rate at a specific point in time. It is not an average velocity. It is most always referred to as "instantaneous velocity."
Velocity can be calculated directly knowing the position of an object at two different points in time. Instantaneous velocity requires that you know the mathematical function that defines the displacement or the displacement rate of the object as a function of time.
Velocity is defined mathematically as the distance traveled (displacement) divided by the time to travel the distance. The instantaneous velocity at a specific point in a time interval is defined by the first derivative of the mathematical function that defines the displacement of the object as a function of time.
The equation for calculating velocity is:
V = (R1 - R2)/(T1-T2)
where V is the velocity or average velocity; R1 is the position in space of the object at a point in time T1;T1 is the point in time when the object is at position R1;
R2 is the position in space of the object at a point in time T2; T2 is the point in time when the object is at position R2.
Instantaneous velocity is calculated by taking the first derivative of the function that defines displacement as a function of time at a specific point in time.
V = lim (r(t+ DeltaT) = r(t))/DeltaT as DeltaT approaches zero(0)
where r(t) is the function that defines the displacement as a function of time; DeltaT is the difference between two points in time at which the displacement is calculated for the displacement function r(t); t is a point in time when the displacement is calculated with the function r(t).