# How does instantaneous velocity differ from average velocity?

##### 1 Answer

*The instantaneous velocity is the specific rate of change of position (or displacement) with respect to time at a single point #(x,t)#, while average velocity is the average rate of change of position (or displacement) with respect to time over an interval.*

Graphically, the **instantaneous velocity** at any given point on a function **tangent line** to the function at that location. Meanwhile, the **average velocity** is equal to the slope of the **secant line** which intersects the function at the beginning and end of the interval.

Typically, when confronted with a problem, it will be fairly evident whether instantaneous velocity or average velocity is called for. For example, suppose Timothy is moving along a track of some kind. Assume that Timothy's displacement function

If asked to find Timothy's velocity *at a given point*, instantaneous velocity would fit best. Thus, at a given point

If asked to find Timothy's average velocity over the course of

In this case,

Note that this leads to dividing by zero in cases where