Average Velocity

Velocity is uses to describe the speed and direction of an object.  If we know the object's speed at a certain time as well as the direction it faces, then we can predict where it will be in the future.

A common way to determine the velocity of an object is to find its average velocity ($\vec{v}_{avg}$) - the distance ($\Delta \vec{r}$) it has traveled divided by the elapsed time ($\Delta t$) it took to travel.

$$\vec{v}_{avg} = \frac{\Delta \vec{r}}{\Delta t}$$

This equation can be rearranged to determine the distance traveled, $\Delta \vec{r} = \vec{v}_{avg}\times \Delta t$, and time elapsed, $\Delta t = \frac{\Delta \vec{r}}{\vec{v}_{avg}}$.

In a situation where the rate of change of velocity is not constant, we instead use the equation:$$\vec{v}_{avg} = \frac{\sum\limits_{i=1}^n \vec{v}_i}{n}$$