<< Chapter < Page Chapter >> Page >

Displacement and distance

Displacement

Displacement is the change in an object's position.

The displacement of an object is defined as its change in position (final position minus initial position). Displacement has a magnitude and direction and is therefore a vector. For example, if the initial position of a car is x i and it moves to a final position of x f , then the displacement is:

x f - x i

However, subtracting an initial quantity from a final quantity happens often in Physics, so we use the shortcut Δ to mean final - initial . Therefore, displacement can be written:

Δ x = x f - x i
The symbol Δ is read out as delta . Δ is a letter of the Greek alphabet and is used in Mathematics and Science to indicate a change in a certain quantity, or a final value minus an initial value. For example, Δ x means change in x while Δ t means change in t .
The words initial and final will be used very often in Physics. Initial will always refer to something that happened earlier in time and final will always refer to something that happened later in time. It will often happen that the final value is smaller than the initial value, such that the difference is negative. This is ok!
Illustration of displacement

Displacement does not depend on the path travelled, but only on the initial and final positions ( [link] ). We use the word distance to describe how far an object travels along a particular path. Distance is the actual distance that was covered. Distance (symbol D ) does not have a direction, so it is a scalar. Displacement is the shortest distance from the starting point to the endpoint – from the school to the shop in the figure. Displacement has direction and is therefore a vector.

[link] shows the five houses we discussed earlier. Jack walks to school, but instead of walking straight to school, he decided to walk to his friend Joel's house first to fetch him so that they can walk to school together. Jack covers a distance of 400 m to Joel's house and another 500 m to school. He covers a distance of 900 m . His displacement, however, is only 100 m towards the school. This is because displacement only looks at the starting position (his house) and the end position (the school). It does not depend on the path he travelled.

To calculate his distance and displacement, we need to choose a reference point and a direction. Let's choose Jack's house as the reference point, and towards Joel's house as the positive direction (which means that towards the school is negative). We would do the calculations as follows:

Distance ( D ) = path travelled = 400 m + 500 m = 900 m
Displacement ( Δ x ) = x f - x i = - 100 m + 0 m = - 100 m

You may also see d used for distance. We will use D in this book, but you may see d used in other books.

Joel walks to school with Jack and after school walks back home. What is Joel's displacement and what distance did he cover? For this calculation we use Joel's house as the reference point. Let's take towards the school as the positive direction.

Distance ( D ) = path travelled = 500 m + 500 m = 1000 m
Displacement ( Δ x ) = x f - x i = 0 m + 0 m = 0 m

It is possible to have a displacement of 0 m and a distance that is not 0 m . This happens when an object completes a round trip back to its original position, like an athlete running around a track.

Interpreting direction

Very often in calculations you will get a negative answer. For example, Jack's displacement in the example above, is calculated as - 100 m . The minus sign in front of the answer means that his displacement is 100 m in the opposite direction (opposite to the direction chosen as positive in the beginning of the question). When we start a calculation we choose a frame of reference and a positive direction. In the first example above, the reference point is Jack's house and the positive direction is towards Joel's house. Therefore Jack's displacement is 100 m towards the school. Notice that distance has no direction, but displacement has.

Differences between distance and displacement

The differences between distance and displacement can be summarised as:

Distance Displacement
1. depends on the path 1. independent of path taken
2. always positive 2. can be positive or negative
3. is a scalar 3. is a vector
4. does not have a direction 4. has a direction

Point of reference

  1. Use [link] to answer the following questions.
    1. Jill walks to Joan's house and then to school, what is her distance and displacement?
    2. John walks to Joan's house and then to school, what is his distance and displacement?
    3. Jack walks to the shop and then to school, what is his distance and displacement?
    4. What reference point did you use for each of the above questions?
  2. You stand at the front door of your house (displacement, Δ x = 0 m ). The street is 10 m away from the front door. You walk to the street and back again.
    1. What is the distance you have walked?
    2. What is your final displacement?
    3. Is displacement a vector or a scalar? Give a reason for your answer.

Questions & Answers

who was the first nanotechnologist
Lizzy Reply
k
Veysel
technologist's thinker father is Richard Feynman but the literature first user scientist Nario Tagunichi.
Veysel
Norio Taniguchi
puvananathan
Interesting
Andr
I need help
Richard
anyone have book of Abdel Salam Hamdy Makhlouf book in pdf Fundamentals of Nanoparticles: Classifications, Synthesis
Naeem Reply
what happen with The nano material on The deep space.?
pedro Reply
It could change the whole space science.
puvananathan
the characteristics of nano materials can be studied by solving which equation?
sibaram Reply
plz answer fast
sibaram
synthesis of nano materials by chemical reaction taking place in aqueous solvents under high temperature and pressure is call?
sibaram
hydrothermal synthesis
ISHFAQ
how can chip be made from sand
Eke Reply
is this allso about nanoscale material
Almas
are nano particles real
Missy Reply
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
Lohitha
where is the latest information on a no technology how can I find it
William
currently
William
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
STM - Scanning Tunneling Microscope.
puvananathan
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
Privacy Information Security Software Version 1.1a
Good
Richard is sitting on his chair and reading a newspaper three (3) meters away from the door
Jeo Reply
The fundamental frequency of a sonometer wire streached by a load of relative density 's'are n¹ and n² when the load is in air and completly immersed in water respectively then the lation n²/na is
Mukesh Reply
Properties of longitudinal waves
Sharoon Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Siyavula textbooks: grade 10 physical science [caps]. OpenStax CNX. Sep 30, 2011 Download for free at http://cnx.org/content/col11305/1.7
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Siyavula textbooks: grade 10 physical science [caps]' conversation and receive update notifications?

Ask