# Speed and Velocity

# Speed and Velocity

**Introduction:**In your everyday life, you may have heard the words "speed" and "velocity" used as if they were synonyms. The problem with doing this is that

**speed**refers to a

**scalar quantity**, or a quantity with only a magnitude (number) associated with it, while

**velocity**refers to a

**vector quantity**, or a quantity with both a magnitude and a direction. The equation for speed and velocity can be summarized by the following:

[math]bar v = d/t[/math], where d=displacement when v=velocity, and d=distance when v=speed

Based on the information presented in the above equation, it is clear to see that

**average velocity**refers to displacement over time, or the change of position with a given magnitude in a given direction over a specified amount of time. On the other hand,**average speed**refers to distance over time, or the change in position with only a given magnitude over a specified amount of time. For example, the average velocity for a car might be 40 meters per second__south__, whereas the average speed for a car would be 40 meters per second.Because average speed equals distance over time and average velocity equals displacement over time, average speed can be found by determining the slopes on a plot of distance vs. time, and average velocity can be found by determining the slopes on a plot of displacement vs. time. This relationship shows that slope relates to the division of the y-axis by the x-axis.

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