Distance is generally used to refer separation between two things. It has a more precise definition in **physics** as, the physical length of separation between two points. We use the **Google maps distance **many times while travelling. In physics, we need to **calculate distance** between various points in order to find important information. There is another term **displacement** that generally refers to the shortest distance between two points. Here we have given **10 examples of distance and displacement** for complete understanding.

## Difference between Distance and Displacement

The SI **units** of distance and displacement are same, meter. But distance is a scalar quantity that refers to the **path length** covered by an object. Displacement is a vector quantity that refers to the difference in the initial and final position of the object.

Through the following points it will get clear to us on **how is displacement different from distance**.

We can **find distance formula**, by considering the distance covered by an object in unit time. This gives us

### * Distance= Speed x Time*

The **displacement formula **is different from that of distance.

When we **differentiate** displacement, the result is velocity (which refers to both speed and direction of the object).

Here, we should note that distance is always positive whereas displacement can be negative or positive.

We will see some of the **examples of** distance and displacement in the following section.

# 10 Examples of Distance and Displacement

(1) A runner starts at the start line and runs 100 meters on a straight lane to complete the race. Let us find the distance travelled and displacement of the runner.The runner runs on a straight path in a single direction. Thus his displacement and distance travelled will be same, and equal to 100 meters.

(2) A car starts from home and travels *40 kilometers* to a hospital and returns back *20 km* to a grocery. Let us consider the distance travelled and displacement of the car.

Distance travelled in this case will be * 40+20=60 kms.*

Displacement =* 40-20=20 kms.*

(3) In the above example, consider that the car starts from home to cover *40 kms* till hospital and returns back to home.

Distance travelled will be *40 kilometers* till hospital plus *40 kms* back to home, equaling to *80 kms.*

Since the car returns back to its original position, there is zero displacement.

(4) Starting from rest, a person moves *20km* west, then *30kms* north from there, and turn east and moves *20kms.*

Displacement will be the difference between the final position and the initial position of the person.In this case, the distance will be the total path travelled which is, *20+30+20=70.*

Finally, the person will be *30 km* north from its starting position. Thus, its displacement is *30km* towards north.

(5) An object starts from A and reaches C. Find its distance and displacement.

Distance= *AB +BC = 20 kms +20 kms* = *40 kilometers.*

Displacement =AC

We can see that since AB is perpendicular to BC, AC is the hypotenuse.

AC =Displacement = *28.2 km* from A to C

(6) In following figure, object starts from A to B to C to D to A.

Distance of the sum *AB+BC+CD+DA=20m+30m+20m+30m= 100 meters*

Since the object starts from A and reaches back to A, its displacement is zero.

(7) If a satellite makes one revolution about the earth. What would be the total distance travelled by it, also find the displacement.

Radius of earth=6,371 kilometers *( Assume satellite revolves around this diameter)*

The distance covered by a satellite in revolution would be equal to the circumference of earth.

Thus given the radius of earth, its circumference will be = *2π x radius of earth*

Distance travelled= *2π x 6,371 kilometers* = *40,07 kilometers*

In one revolution the satellite comes back to the place from where it started, thus its **displacement will be zero**.

(8) In the above question, let us consider the satellite makes one and a half revolution. Let us find the distance travelled and displacement in this case.

The distance travelled will be = *2πr +2πr/2 = 40,07 km + 20,03 km= 6010 km*

The displacement will be the shortest distance between the final and initial position of the satellite. The satellite is diametrically opposite to earth, therefore the **displacement will be equals to the diameter of earth**.

Thus, displacement = 2 x radius of earth = *2 x 6,371 km = 12742 km.*

(9) Consider a car moving at a speed of *30km/h* for duration of *2 hours* in a straight road. What will be the distance travelled and displacement?

Since, *Distance = Speed x Time*

Therefore, distance travelled by the car will be *30km/h x 2h = 60km*.

Since the particle is travelling in a linear direction, its displacement will be equal to its distance travelled, equals to *60km*.

(10) Now consider the car moves in a direction for 2 hours at *30km/h* and returns back and travels at *20km/h* for *1 hour*. Let us find the distance travelled and the displacement of the car.

The distance travelled by the car will be *30km/h x 2h + 20km/h x 1h =60km +20km = 80km.*

Displacement = *60km – 20km = 40km* from the position of start.