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# 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:

$bar v = d/t$, 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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