# Basic Physics Lesson-1 : Distance and Displacement

*Umesh is a freelance writer contributing his creative writings on varied subjects in various sites and portals in the internet.*

## Introduction

Physics is the branch of science in which we study the nature and properties of material and energy and for all such things formulas of Physics are derived for calculation purposes. Physics is deeply related to Mathematics and Chemistry and together these three subjects make a robust scientific understanding. This is the first article in the basic Physics learning series and in this series we will try to understand basic physics and its applications. In the present article, we will try to learn the distance and displacement. Though this is a beginners course but it might also interest the science students, professionals, and scientists to revise their basic concepts.

## What do we understand by distance?

When someone says that he or she has walked a distance of 5 km today, what does it mean to us? It simply tells us that he has walked from one place to another whatever path he has chosen among the streets or lanes or maybe many rounds in a big park or playground. Whatever path, a straight line or zig-zag one he has followed, the net result is that he has walked a total of 5 km. Can we say in which direction he walked? No, he went sometimes in one direction and sometimes in another so we do not know the direction. It was changing during the course of his walking.

So, we know the total length of the path he had traversed during his walk and it was 5 km. In Physics, we call such quantities as scaler quantities. They do have a value but do not have a direction.

## What do we understand by displacement?

What happens when we add an element of direction to the distance? Then it becomes a vector quantity. Let us understand it better with the example of the person who walked 5 km on that day. Let us see how he went on. We have to consider each element of his walk. Suppose in the first leg of his walk he walked 200 m in an Easterly direction. Now this distance of 200 m has got a direction element attached to it. In Physics we call such quantities a vector - they have a value as well as direction. So this distance of 200 m in East direction is known in Physics as a displacement of 200 m in the East direction. We can represent it as a line drawn to the scale in the East direction. For the understanding purpose, we put an arrow at the end of it to show the direction which is of course towards East in this particular case.

## Pictorial representation

All the part distances walked by a person in a particular direction can be treated as a displacement vector and can be represented with a value and direction. So the path traversed by him will be a sum of so many vectors annexed with one another.

Let us extend the same example now. As we know that the person first walked 200 m in the East direction. Now let us assume that after that he walked 300 m in North-East direction and completed some work there and then went a distance of 400 m Southwards. We can show these three displacements as vectors (diagram-1).

## Diagram - 1

## Application - example

Once we understand the notion of displacement then we can use it in solving different types of problems related to displacement. Let us take the above example and extend it further. Let us give the names of the different points along the walk of the person as A, B, C, D, and E. Of course, A is the starting point.

So, the person has already walked 200 m from point A to B in the East direction and then 300 m from B to C in the North-East direction and then walked 400 m from C to D in the South direction. Now let us assume that he further walks 100 m from D to E in the West direction to a cafeteria for a cup of coffee.

The problem is to find where the cafeteria lies with respect to point A from where he started.

To solve this problem one has to draw the displacements on a scale and measure the distance of the point E from A on the same scale and the exact direction can be found with a compass. I have drawn it and found that displacement AE has a value of about 360 m and is almost in a South-East direction of the starting point A. The solution is given in diagram-2.

Though the person had walked a total distance of 200 + 300 + 400 + 100 = 1000 m but his displacement from the starting point A is only about 360 m.

This displacement can also be understood in terms of vector addition where AB, BC, CD, and DE all are vectors having some magnitude and direction. When we draw the vectors in that fashion then it is actually a vector addition and is mathematically represented as -

AE = AB + BC + CD + DE

Please note that above is not a simple arithmetic addition but is a vector addition. Another important thing is that a vector is written from the point it starts to the point it ends. For example if we write a vector starting from B to A then it will be written as BA which is equal to vector AB in magnitude but not in direction. Actually its direction is opposite to the direction of AB which in vector algebra simply means and written as -

BA = - AB

## Diagram - 2

## Conclusion

Distance is a scalar quantity and tells the total length of the path traversed while displacement is a vector quantity that specifies a value and its direction for each element of that path traversed.

## References

1. https://www.khanacademy.org/science/physics/one-dimensional-motion/displacement-velocity-time/a/what-is-displacement&hl=en-IN

2. https://physics.info/displacement/&hl=en-IN

*This content is accurate and true to the best of the author’s knowledge and is not meant to substitute for formal and individualized advice from a qualified professional.*

**© 2020 Umesh Chandra Bhatt**

## Comments

**Umesh Chandra Bhatt (author)** from Kharghar, Navi Mumbai, India on April 16, 2020:

G C Joshi, thanks a lot.

**Umesh Chandra Bhatt (author)** from Kharghar, Navi Mumbai, India on April 14, 2020:

Dr Ashok, thanks for your lovely comment.

**Umesh Chandra Bhatt (author)** from Kharghar, Navi Mumbai, India on April 14, 2020:

SKMUNSHI, so kind of you for visiting my articles often. Highly appreciate.

**Umesh Chandra Bhatt (author)** from Kharghar, Navi Mumbai, India on April 14, 2020:

Sangita, thanks for encouragement.

**Umesh Chandra Bhatt (author)** from Kharghar, Navi Mumbai, India on April 14, 2020:

Aktiwari1201, thanks a lot for your nice comment.

**SKMUNSHI** on April 13, 2020:

Well begun ,Nice introduction & quite refreshing along with pictorial description 0f distance and displacement. A brief introduction to fundemental SI units used in physics may be considered.

**Sangita** on April 13, 2020:

Very nice! I must make achchu read it - will be very useful for her!

**aktiwari1201** on April 13, 2020:

Really interesting and refreshing article on distance and displacement. Though I had been a science student yet I find this article will make the non science students to understand the difference. Nicely depicted diagrams to tell the difference between vector and scaler.

Keep posting!

**Umesh Chandra Bhatt (author)** from Kharghar, Navi Mumbai, India on April 03, 2020:

Cynthia, thanks for your nice comment.

**Cynthia Zirkwitz** from Vancouver Island, Canada on April 03, 2020:

I actually did not study physics at any (knowing, formal) time, but in my old age it seems like it might be at least somewhat cognitively useful to spend some time and energy learning a little about this science. Thank you for making this lesson interesting and graspable.

**Umesh Chandra Bhatt (author)** from Kharghar, Navi Mumbai, India on March 21, 2020:

Juliette, thanks for your comment. Appreciate. Keep in touch.

**Juliette Kando FI Chor** from Andalusia, southern Spain on March 21, 2020:

Very clear explanation of basic physics terminology,

**Umesh Chandra Bhatt (author)** from Kharghar, Navi Mumbai, India on March 01, 2020:

Anurag, thanks for visiting and your nice comment. Appreciate.

**Anurag** on March 01, 2020:

Really nice and inspiring article for everyone who keeps interest in scientific era!!

Not only children but also a refreshing article for people who have interest in Physics but somehow gets busy in there day to day life!!

Keep posting new!!

**Umesh Chandra Bhatt (author)** from Kharghar, Navi Mumbai, India on February 27, 2020:

Liz, I would be trying to write similar ones in sequence and they would definitely interest you. Thanks for your visit and I appreciate much.

**Umesh Chandra Bhatt (author)** from Kharghar, Navi Mumbai, India on February 27, 2020:

Prantika, thanks for your interest in Physics and thanks for your visit. Appreciate

**Liz Westwood** from UK on February 27, 2020:

This takes me back to the basic physics I studied many years ago.

**Prantika Samanta** from Kolkata, India on February 27, 2020:

A wonderful and interesting article. I loved physics during my school days. Good to read again the physics article.

**Umesh Chandra Bhatt (author)** from Kharghar, Navi Mumbai, India on February 26, 2020:

Peggy, thanks a lot for your appreciation and good words. Also for sparing your time and extending your concern.

**Umesh Chandra Bhatt (author)** from Kharghar, Navi Mumbai, India on February 26, 2020:

Flourish, thanks for your nice comment. I am encouraged in my humble attempt.

**Umesh Chandra Bhatt (author)** from Kharghar, Navi Mumbai, India on February 26, 2020:

AL, thanks for visiting. Many science subjects do not attract the fancy of many. But they have their own strengths in humanities and arts. It is the interest that takes us there. Be in touch.

**Peggy Woods** from Houston, Texas on February 26, 2020:

Thanks for this introduction to physics. I never took it in school. Beyond basic math, I only studied algebra 1, algebra 2, and geometry. Your explanation and drawing made sense to me, so kudos to you for this lesson.

**FlourishAnyway** from USA on February 26, 2020:

This brings back memories of high school physics class! The basics I got, but anything more not so much.

**AL** on February 26, 2020:

Thanks for sharing some basics in physics Umesh.

I never liked the calculation part of any science including physics, I still don't. Scalar and Vector calculations were the basics but somehow still gave me headaches.

**Umesh Chandra Bhatt (author)** from Kharghar, Navi Mumbai, India on February 26, 2020:

Jay, first of all I thank you for your visit to this basic article. Your question is of advanced nature but with my little knowledge of Astrophysics I can only say that in the galaxies the stars along with their planets are so distantly repeat distantly situated that collision of two galaxies is not a collision but passing through each other. Still, there could be some head ons though it would had been a rarity. There could be some gravitational interactions when the massive bodies were passing but that would be of insignificant nature seeing the astronomical distances.

**Umesh Chandra Bhatt (author)** from Kharghar, Navi Mumbai, India on February 26, 2020:

Eric, thanks for your stopping by. Yes, back and forth is a distance because we have traversed it. But our displacement is zero. We are where we started. Remember displacement is a vector. If you have interest in Physics, we would have these things again when I come up with future lessons on using vector addition or substraction of velocities, forces etc.

**Jay C OBrien** from Houston, TX USA on February 26, 2020:

How would you calculate the effect of a galactic collision? 700 mya the Dwarf Galaxy Sagitarius collided with the Milky Way and has since circled around it. The Earth was at the impact point. Did the collision change our solar system? A geologist says no, what do you think?

**Eric Dierker** from Spring Valley, CA. U.S.A. on February 26, 2020:

Just a quickie for now. Is back and forth a distance?