Distance and Displacement

Often, we are unable to understand and differentiate between the similar terms distance and displacement. They may seem to have a very similar meaning and are often used to denote each other. However, there are subtle differences between them, which have a major effect when used in the field of Physics. Let us try to understand how they are different from one another. 

What is Distance?

For a body that has moved from its initial position, the total distance covered is the total length of the path covered by it when moving from its initial position to its final position. Distance covered by a body does not always need to be a straight-line path and it may not be the shortest length between two points. Let us take an example to understand the concept of distance. 

Mr. Margo is initially at rest at Point A and then moves 15 meters towards the north. He turns right and moves 12 meters more. He then decides to take a right turn and travel 10 meters more to reach Point B. The path taken by Mr. Margo can be shown with the diagram below. The total distance covered by  distance covered by Mr. Margo is the sum of the lengths of the paths he has moved. 

So, total distance covered = (15+12+10) meters = 37 meters

What is Displacement?

For a body which has moved, the minimum length from the starting point to the endpoint is known as the displacement of the body. Displacement is always measured in a straight line, irrespective of the path taken for the movement. Let us understand the concept of displacement with the example below. 

Mr. Margo is initially at rest at Point A and then moves 30 meters towards the north. He turns right and moves 40 meters more to reach Point B. Then the path taken can be shown in the diagram below. The displacement of Mr. Margo is represented with the dotted lines.  The displacement of Mr. Margo is represented with the dotted lines. 

Distance and Displacement: Physical Differences

There are some physical differences between distance and displacement which are listed below. 

1. While distance is a scalar quantity, displacement is a vector quantity. This means that distance does not have any direction, and has a magnitude only. However, in the case of displacement, it has both a magnitude and a direction. 
2. Since displacement has a direction, it can have a negative value. However, for distance, a negative value is not possible.
3. Distance is path-dependent while displacement is path-independent. This means, for a body, the path taken while moving determines its distance, while displacement is the straight-line length between the initial and the final positions. 

Distance and Displacement: Relationship with Time

Both the distance and displacement of a body are dependent on time. However, in the case of distance, as time goes on, it can never decrease with time. However, the displacement of a body can decrease with time. 

Since displacement is the shortest distance between two points, it can decrease with time if the body in motion decides to take a winding path. However, the more winding a path is, the more distance is covered by the body.

Distance and Displacement: Formula and Denotation

The formula for distance is as follows:

distance(d)=speed(v)time(t)

The formula for magnitude of displacement is as follows:

displacement(s) = velocity(v)time(t)

When carrying out calculations in Physics or other related fields, then the distance covered by a body in motion is represented by the letter d.

In calculations involving the displacement of a body in motion, the representation is done using the letter s with an arrow over it to show that it is a vector. If only the magnitude of displacement is to be considered, we represent it using s.

Conclusion

Now that you have a pretty good understanding of the differences between distance and displacement, you should be able to understand their uses. Just like distance and displacement, there are several other such terms that have a similar meaning but have major differences when used in a particular concept. How they are used has major implications on calculations and understanding, where mistakes cannot be tolerated.