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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

Aim:

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

Apparatus:

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

Method:

  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

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
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
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
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
Praveena Reply
hi
Loga
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
how did you get the value of 2000N.What calculations are needed to arrive at it
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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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