Ideally, we would always know where an object is located and how it is moving at every point in time. However, the motion of an object may be incredibly complicated, so that describing the position or velocity of an object at all points in time in an equation might be difficult it not impossible.  It may also be the case that we just don’t have enough information to describe the motion of an object at any point in time we want.  We may only know how an object is moving at several distinct points in time.  Instead of being able to watch a movie which shows how an object moves, we only have a limited number of snapshots when we know where the object is and what is its velocity.

So how can we describe the motion of an object if we don’t have an equation that tells us how it is moving at every point in time?  We can describe how the object is moving on average.  If we don’t know what an object’s motion is at every point in time, we can still report how the object’s position and velocity have changed between two points in time.  We can then use the change in position and change in velocity vectors to calculate the object’s average velocity or average acceleration over a time interval.