# Velocity Formula Study Guide

## Velocity

Velocity is a *vector* quantity. In other words, velocity measures not only speed, but the direction that an object is traveling as mentioned in the study guide on motion .

Much as instantaneous speed can be measured using a speedometer, so can instantaneous velocity be measured. The velocity unit would include the speed traveled as well as the direction traveled in. For instance, a car going east with a speedometer reading of 30 mph would be written as 30 mph E or 30 mph east

## Velocity Formula

The average velocity formula is very simple to use if you know how to use the speed formula and you understand the concept of velocity. Don’t forget the average speed formula does not take into account any change in direction, which would have to be taken into account for the velocity answer. An example is given below.

- A car travels 20 m/s north (where m=meters and s=seconds), then turns east and travels 40 m/s. These are constant measurements, which means they are also equal to the average speed. However, if you only wanted the average speed of the trip, you would have to combine the two measurements to get the total, the divide. Since we already know the average speed of each direction, we simple add them together and divide by 2 because there are 2 units that we are working with. The average speed of the entire trip would be written as (20 m/s + 40m/s)/2 and the answer would be 30 m/s because 20+40=60. 60/2=30.

However, to find the average velocity, you would simply use the units already given. You cannot combine the two because they are in different directions and velocity changes with a direction change. Let’s try another one with no change in direction.

- A car traveled 70 meters in the northern direction for 10 minutes. Find the velocity.
- Before beginning any formula, you need to find the standard units. When dealing with meters, the standard unit is seconds. Therefore, the first thing we need to do is to change the minutes to seconds by multiplying the amount of minutes by 60. 10 times 60 is 600. The car traveled 70 meters north in 600 seconds.
- Use the formula for average speed to find the average velocity. (This is possible because the speed is in the same direction the entire time.)
- average speed= distance traveled/ time to travel distance so average speed= 70m/600s
- 70m/600s= .12 m/s after rounding off to significant numbers.

Keep in mind that you can always use the speed formula to figure out the velocity, but only going one direction at a time. Direction is the main difference between velocity and speed.