# 0.2 Motion in one dimension  (Page 4/16)

 Page 4 / 16

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. 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, $\Delta x=0\phantom{\rule{2pt}{0ex}}\mathrm{m}$ ). The street is $10\phantom{\rule{2pt}{0ex}}\mathrm{m}$ 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.

## Speed, average velocity and instantaneous velocity

Velocity

Velocity is the rate of change of displacement.

Instantaneous velocity

Instantaneous velocity is the velocity of a body at a specific instant in time.

Average velocity

Average velocity is the total displacement of a body over a time interval.

Velocity is the rate of change of position. It tells us how much an object's position changes in time. This is the same as the displacement divided by the time taken. Since displacement is a vector and time taken is a scalar, velocity is also a vector. We use the symbol $v$ for velocity. If we have a displacement of $\Delta x$ and a time taken of $\Delta t$ , $v$ is then defined as:

$\begin{array}{ccc}\hfill \mathrm{velocity}\phantom{\rule{4pt}{0ex}}\left(\mathrm{in}\phantom{\rule{4pt}{0ex}}\mathrm{m}·{\mathrm{s}}^{-1}\right)& =& \frac{\mathrm{change}\phantom{\rule{4pt}{0ex}}\mathrm{in}\phantom{\rule{4pt}{0ex}}\mathrm{displacement}\phantom{\rule{4pt}{0ex}}\left(\mathrm{in}\phantom{\rule{4pt}{0ex}}\mathrm{m}\right)}{\mathrm{change}\phantom{\rule{4pt}{0ex}}\mathrm{in}\phantom{\rule{4pt}{0ex}}\mathrm{time}\phantom{\rule{4pt}{0ex}}\left(\mathrm{in}\phantom{\rule{4pt}{0ex}}\mathrm{s}\right)}\hfill \\ \hfill v& =& \frac{\Delta x}{\Delta t}\hfill \end{array}$

Velocity can be positive or negative. Positive values of velocity mean that the object is moving away from the reference point or origin and negative values mean that the object is moving towards the reference point or origin.

An instant in time is different from the time taken or the time interval. It is therefore useful to use the symbol $t$ for an instant in time (for example during the 4 th second) and the symbol $\Delta t$ for the time taken (for example during the first 5 seconds of the motion).

Average velocity (symbol $v$ ) is the displacement for the whole motion divided by the time taken for the whole motion. Instantaneous velocity is the velocity at a specific instant in time.

This is terminology that occurs quite often and it is important to always remember that instantaneous and average quantities are not always the same. In fact, they can be very different. The magnitude of the instantaneous velocity is the same as the slope of the line which is a tangent to the displacement curve at the time of measurement. The magnitude of the average velocity is the same as the slope of the line between the start and end points of the interval.

If you want to think about why the tangent at a particular time gives us the velocity remember that the velocity is the slope of the displacement curve. Now, a simple why to start thinking about it is to image you could zoom (magnify) the displacement curve at the point. The more you zoom in the more it will look like a straight line at the point and that straight line will be very similar to the tangent line at the point. This isn't a mathematical proof but you will learn one later on in mathematics about limits and slopes.

do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
Do somebody tell me a best nano engineering book for beginners?
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
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
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
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
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!