Tuesday , August 22 2017
Calculators

10 Examples of Distance and Displacement

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.

example of displacement
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.

displacement

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

example of distance

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.                                                                                                                                                      difference of distance and dispalcement

   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= \sqrt{20^2+20^2}

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.

Authored by Kiran Mandia

I am a computer science student at Indian Institute of Technology, Kharagpur; and a writer who loves to read about various topics.I also like making short films.

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