# Examples of Displacement: Exhaustive and Detailed Analysis

Displacement is a vector of distance and direction in geometry and mechanics.

The shortest distance between two points is the length of the displacement vector. Because displacement is a vector, it accounts for both the magnitude and direction of motion in a straight line between the start and end points of a trajectory. The unit of displacement is meters in the SI unit system.

Let us look at some common yet diverse examples of displacement to understand this concept better.

## A teacher walking across the blackboard

If a teacher paces back and forth across the blackboard multiple times, they tend to cover a more considerable distance than the actual magnitude of the displacement.

This is because the displacement is calculated as only the shortest path length from the start to the end point. Let us consider that the teacher starts from 1.2 m as the initial point and stops at 3.2 m on the right. Then the displacement covered is ∆x = 3.2 m – 1.2 m = + 2.0 m. The positive sign signifies motion in the right direction of the coordinate system, whereas the negative sign denotes motion in the left direction. Examples of Displacement: Teacher walking across blackboard; Image Source: Openstax College Physics

## Passenger walking relative to the airplane

Let us consider a passenger moving to the rear end relative to the airplane as another of the examples of displacement. Examples of Displacement: Passenger walking in airplane; Image Source: Openstax College Physics

If a passenger starts from 5.0 m, travels to the rear end of the plane, and stops at 2.0 m, then the displacement equals ∆x = 2.0 m – 5.0 m = – 3.0 m. The negative sign denotes that the person has traveled in the negative direction of the coordinate system.

## Motion parallel to the latitude

Motion in the direction parallel to the latitude of the Earth can also signify displacement.

Let’s say we rented one of those massive helicopters and attached it to the Eiffel Tower in order to transport it to Vienna, Austria. This signifies displacement of an enormous icon moving over a distance of 1,033.81 km due east along the 48th parallel of latitude.

## Moving candle-stick on the table

Let us imitate the above example by moving a candle from one side to another side of a table.

Suppose a candle is moved move from 1.0 m on the table to 2.5 m in the east direction. Hence the displacement covered the candle is ∆x = 2.5 m – 1.0 m = – 1.5 m. In this situation, movement in the east direction is considered a positive movement, just like movement in the right in the above examples.

## Jogger on a jogging track

Let us take the example of a jogger on a jogging track. Examples of Displacement: Jogger on a jogging track; Image Source: Image by Manfred Richter from Pixabay

Suppose the jogger runs 50 m east before realizing that he has lost his phone somewhere on the track. He returns 45 m to the west to find it. He covers another 60 m before turning around to resume his jog in the eastward direction. Although he has run a distance of 50 m + 45 m + 50 m = 145 m, his total displacement is 55 m towards the east.

## Cross-country skier

Consider the diagram below of a cross-country skier at different instants of time. Examples of Displacement: Cross-country skier; Image Source: Self Image

The skier takes a U-turn and starts moving in the opposite direction at every indicated time. In an overview, the skier travels from point A to B to C and finally stops at point D. It can be observed that the skier covers a displacement of 140 m towards the right of the coordinate system.

## Football coach pacing along the sidelines

Let us consider a football coach pacing back and forth along the sidelines of the football ground. Examples of Displacement: Football coach pacing along sidelines; Image Source: Self Image

The diagram above denotes the instantaneous position of the coach at various indicated times. He starts moving from one marked point and then reverses his direction at every next marked point. Despite covering a pretty significant distance, the coach covers a displacement of only 55 m towards the left.

## Child playing in a rectangular field

Suppose a child decides to run along the edges while playing in a rectangular field.

The child in this example starts running from one corner of the field and finishes up at the same one. Since the initial point in his path is the same as the final point, the displacement covered by the child is equal to zero.

## Biker on a horizontal hoop

Suppose a biker rides in a horizontal hoop of radius 15 m and covers 3/4th of the same as in the diagram below. Examples of Displacement: Biker on horizontal loop; Image Source: Self Image

The displacement is calculated as the length of the shortest straight-line path between the start and the end points. Hence from the diagram above, ∆x = √2 x radius = 15√2 m.

## Frequently Asked Questions (FAQs)

### Q: Is displacement a scalar or a vector quantity?

A: Displacement is a vector quantity because it accounts for both magnitude and direction.

### Q: Can an object travel a distance equal to the magnitude of the displacement covered by it?

A: Yes, an object can cover a displacement equal to that of the distance covered if it travels in a straight-line path with no change in its direction.

### Q: Can an object have covered zero displacement despite having moved through a distance? If yes, support your answer with an example.

A: Yes, if an object covers a circular path, having the start point as the same as the end point, then the displacement covered becomes zero; despite the distance being equal to the circumference of the circular path.

### Q: Can the displacement covered by an object be negative?

A: Since displacement is a vector that accounts for both magnitude and direction, it can also exhibit negative sign to signify negative movement in the coordinate system.

Esha Chakraborty

I have a background in Aerospace Engineering, currently working towards the application of Robotics in the Defense and the Space Science Industry. I am a continuous learner and my passion for creative arts keeps me inclined towards designing novel engineering concepts. With robots substituting almost all human actions in the future, I like to bring to my readers the foundational aspects of the subject in an easy yet informative manner. I also like to keep updated with the advancements in the aerospace industry simultaneously. Connect with me with LinkedIn - http://linkedin.com/in/eshachakraborty93