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To calculate the velocity of the taxi you need to calculate the gradient of the line at each second:

v 1 s = Δ x Δ t = x f - x i t f - t i = 5 m - 0 m 1 , 5 s - 0 , 5 s = 5 m · s - 1
v 2 s = Δ x Δ t = x f - x i t f - t i = 15 m - 5 m 2 , 5 s - 1 , 5 s = 10 m · s - 1
v 3 s = Δ x Δ t = x f - x i t f - t i = 30 m - 15 m 3 , 5 s - 2 , 5 s = 15 m · s - 1

From these velocities, we can draw the velocity-time graph which forms a straight line.

The acceleration is the gradient of the v vs. t graph and can be calculated as follows:

a = Δ v Δ t = v f - v i t f - t i = 15 m · s - 1 - 5 m · s - 1 3 s - 1 s = 5 m · s - 2

The acceleration does not change during the motion (the gradient stays constant). This is motion at constant or uniform acceleration.

The graphs for this situation are shown in [link] .

Graphs for motion with a constant acceleration (a) position vs. time (b) velocity vs. time (c) acceleration vs. time.

Velocity from acceleration vs. time graphs

Just as we used velocity vs. time graphs to find displacement, we can use acceleration vs. time graphs to find the velocity of an object at a given moment in time. We simply calculate the area under the acceleration vs. time graph, at a given time. In the graph below, showing an object at a constant positive acceleration, the increase in velocity of the object after 2 seconds corresponds to the shaded portion.

v = area of rectangle = a × Δ t = 5 m · s - 2 × 2 s = 10 m · s - 1

The velocity of the object at t = 2 s is therefore 10 m · s - 1 . This corresponds with the values obtained in [link] .

Summary of graphs

The relation between graphs of position, velocity and acceleration as functions of time is summarised in [link] .

Position-time, velocity-time and acceleration-time graphs.

Often you will be required to describe the motion of an object that is presented as a graph of either position, velocity or acceleration as functions of time. The description of the motion represented by a graph should include the following (where possible):

  1. whether the object is moving in the positive or negative direction
  2. whether the object is at rest, moving at constant velocity or moving at constant positive acceleration (speeding up) or constant negative acceleration (slowing down)

You will also often be required to draw graphs based on a description of the motion in words or from a diagram. Remember that these are just different methods of presenting the same information. If you keep in mind the general shapes of the graphs for the different types of motion, there should not be any difficulty with explaining what is happening.

Experiment: position versus time using a ticker timer


To measure the position and time during motion and to use that data to plot a “Position vs. Time" graph.


Trolley, ticker tape apparatus, tape, graph paper, ruler, ramp


  1. Work with a friend. Copy the table below into your workbook.
  2. Attach a length of tape to the trolley.
  3. Run the other end of the tape through the ticker timer.
  4. Start the ticker timer going and roll the trolley down the ramp.
  5. Repeat steps 1 - 3.
  6. On each piece of tape, measure the distance between successive dots. Note these distances in the table below.
  7. Use the frequency of the ticker timer to work out the time intervals between successive dots. Note these times in the table below,
  8. Work out the average values for distance and time.
  9. Use the average distance and average time values to plot a graph of “Distance vs. Time" onto graph paper . Stick the graph paper into your workbook. (Remember that “A vs. B" always means “y vs. x").
  10. Insert all axis labels and units onto your graph.
  11. Draw the best straight line through your data points.

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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Source:  OpenStax, Physics - grade 10 [caps 2011]. OpenStax CNX. Jun 14, 2011 Download for free at http://cnx.org/content/col11298/1.3
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