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Speed, average velocity and instantaneous 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 Δ x and a time taken of Δ t , v is then defined as:

velocity ( in m · s - 1 ) = change in displacement ( in m ) change in time ( in s ) v = Δ x Δ t

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 Δ 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.

(Average) Speed (symbol s ) is the distance travelled ( D ) divided by the time taken ( Δ t ) for the journey. Distance and time are scalars and therefore speed will also be a scalar. Speed is calculated as follows:

speed ( in m · s - 1 ) = distance ( in m ) time ( in s )
s = D Δ t

Instantaneous speed is the magnitude of instantaneous velocity. It has the same value, but no direction.

James walks 2 km away from home in 30 minutes. He then turns around and walks back home along the same path, also in 30 minutes. Calculate James' average speed and average velocity.

  1. The question explicitly gives

    • the distance and time out (2 km in 30 minutes)
    • the distance and time back (2 km in 30 minutes)
  2. The information is not in SI units and must therefore be converted.

    To convert km to m, we know that:

    1 km = 1 000 m 2 km = 2 000 m ( multiply both sides by 2 )

    Similarly, to convert 30 minutes to seconds,

    1 min = 60 s 30 min = 1 800 s ( multiply both sides by 30 )
  3. James started at home and returned home, so his displacement is 0 m.

    Δ x = 0 m

    James walked a total distance of 4 000 m (2 000 m out and 2 000 m back).

    D = 4 000 m
  4. James took 1 800 s to walk out and 1 800 s to walk back.

    Δ t = 3 600 s
  5. s = D Δ t = 4 000 m 3 600 s = 1 , 11 m · s - 1
  6. v = Δ x Δ t = 0 m 3 600 s = 0 m · s - 1

Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
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.
what is the actual application of fullerenes nowadays?
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.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
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.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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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