It is important to note the difference between distance traveled and displacement since, in general, they are different concepts that are often confused. Distance traveled is a scalar magnitude that is measured over the trajectory. Displacement is a vector magnitude that depends only on the initial and final position of the body and which is independent of the trajectory. Imagine a body that moves on a circular path, thus returning to the starting point. The distance traveled by the body will be $2\mathrm{\pi r}$  (the circumference length). In contrast, the displacement vector is 0 because the position vector at the beginning of the movement and the position vector at the end are the same.

The following are some similarities and differences which can be deduced easily from the above.

 Displacement Vector Distance traveled Vector magnitude Scalar magnitude Depends on the initial and final points It depends on the trajectory Its magnitude coincides with the distance traveled when the trajectory is a straight line and there is no change of direction. Its value matches the magnitude of the displacement vector when the trajectory is a straight line and there is no change of direction. Its magnitude increases or decreases with the motion according to the trajectory described Its magnitude always increases when the body is in motion, regardless of the trajectory It is measured in meters It is measured in meters

Experiment and Learn

Data
$\Delta s=$
$\left|\Delta \stackrel{\to }{r}\right|=$
Displacement vs distance traveled

This example shows the trajectory that a body follows, as well as its initial and final positions. Move either one or both red dots and observe how the displacement magnitude and the distance traveled change.

Notice that unless the initial and final positions are very close (almost in a straight line) the distance traveled is greater than the displacement. They will only be equal when they are very close, or the trajectory is a straight line.

## Solved exercises worksheet

Here you can test what you have learned in this section.

#### What do you know about displacement and distance traveled?

difficulty

Answer if the following statements are true or false:

a) Distance traveled only depends on the starting and final positions without consideration of the trajectory.
b) Distance traveled is always greater or equal than the magnitude of the displacement vector.
c) Distance traveled it is a vector.
d) As time passes, a body in motion always increases its displacement.

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