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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

where we get a research paper on Nano chemistry....?
Maira Reply
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
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
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
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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

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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
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