<< 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

how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
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
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 the best Algebra and trigonometry course in your pocket!





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