Chapter 2, Problem 1CQ

Give an example in which there are clear distinctions among distance traveled, displacement, and magnitude of displacement. Specifically identify each quantity in your example.

To determine

An example consisting of clear distinctions among distance traveled, displacement, and magnitude of displacement.

Explanation of Solution

Introduction:

The distance traveled by the student is the total lengthof the path traveled between two positions and the distance is the magnitude of displacement. Note that the distance traveled and the distance are both scalars, that is,just numbers with a length unit. The student’s displacement is the difference between the final and initial position of the student. Since the displacement is a vector, we will have to specify not only its magnitude but direction as well (east / right, west / left, north / up, south / down).

A student walking to her school which is 2 km east from her starting point, then she is moving back 1 km to west from her school.

Let’s start calculating the distance traveled by the student. The student walks 2 km to east, then walks 1 km to west from the school, thus the total length of the path traveled between the initial and final position is

$d_{traveled}=2km+1km=3km$

Consider East to be positive x-axis.

So, the student’s displacement is

$$

$\Delta \overrightarrow{x}=2km\widehat{i}-1km\widehat{i}=1km\widehat{i}$ .

The student’s displacement is $1km$ to the east of her starting position.

Finally, the magnitude of displacement is the distance

$d\equiv \left|\Delta \overrightarrow{x}\right|=\left|1km\widehat{i}\right|=\left|1km\right|\left|\widehat{i}\right|=1km$

Conclusion:

The student’s displacement is 1 km to the east and the distance is 3 km.