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The velocity vs. time graph of a truck is plotted below. Calculate the distance and displacement of the truck after 15 seconds.

  1. We are asked to calculate the distance and displacement of the car. All we need to remember here is that we can use the area between the velocity vs. time graph and the time axis to determine the distance and displacement.

  2. Break the motion up: 0 – 5 seconds, 5 – 12 seconds, 12 – 14 seconds and 14 – 15 seconds.

    For 0 – 5 seconds: The displacement is equal to the area of the triangle on the left:

    Area = 1 2 b × h = 1 2 × 5 s × 4 m · s - 1 = 10 m
    For 5 – 12 seconds: The displacement is equal to the area of the rectangle:
    Area = × b = 7 s × 4 m · s - 1 = 28 m 2

    For 12 – 14 seconds the displacement is equal to the area of the triangle above the time axis on the right:

    Area = 1 2 b × h = 1 2 × 2 s × 4 m · s - 1 = 4 m
    For 14 – 15 seconds the displacement is equal to the area of the triangle below the time axis:
    Area = 1 2 b × h = 1 2 × 1 s × 2 m · s - 1 = 1 m

  3. Now the total distance of the car is the sum of all of these areas:

    Δ x = 10 m + 28 m + 4 m + 1 m = 43 m
  4. Now the total displacement of the car is just the sum of all of these areas. HOWEVER, because in the last second (from t = 14 s to t = 15 s) the velocity of the car is negative, it means that the car was going in the opposite direction, i.e. back where it came from! So, to find the total displacement, we have to add the first 3 areas (those with positive displacements) and subtract the last one (because it is a displacement in the opposite direction).

    Δ x = 10 m + 28 m + 4 m - 1 m = 41 m in the positive direction

The position vs. time graph below describes the motion of an athlete.

  1. What is the velocity of the athlete during the first 4 seconds?
  2. What is the velocity of the athlete from t = 4 s to t = 7 s?

  1. The velocity is given by the gradient of a position vs. time graph. During the first 4 seconds, this is

    v = Δ x Δ t = 4 m - 0 m 4 s - 0 s = 1 m · s - 1
  2. For the last 3 seconds we can see that the displacement stays constant. The graph shows a horisontal line and therefore the gradient is zero. Thus v = 0 m · s - 1 .

The acceleration vs. time graph for a car starting from rest, is given below. Calculate the velocity of the car and hence draw the velocity vs. time graph.

  1. The motion of the car can be divided into three time sections: 0 – 2 seconds; 2 – 4 seconds and 4 – 6 seconds. To be able to draw the velocity vs. time graph, the velocity for each time section needs to be calculated. The velocity is equal to the area of the square under the graph:

    For 0 – 2 seconds:

    Area = × b = 2 s × 2 m · s - 2 = 4 m · s - 1
    The velocity of the car is 4 m · s - 1 at t = 2s.For 2 – 4 seconds:
    Area = × b = 2 s × 0 m · s - 2 = 0 m · s - 1
    The velocity of the car is 0 m · s - 1  from t = 2 s to t = 4 s.For 4 – 6 seconds:
    Area = × b = 2 s × - 2 m · s - 2 = - 4 m · s - 1
    The acceleration had a negative value, which means that the velocity is decreasing. It starts at a velocity of 4 m · s - 1  and decreases to 0 m · s - 1 .

  2. The velocity vs. time graph looks like this:

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.
yes that's correct
I think
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
analytical skills graphene is prepared to kill any type viruses .
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
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.
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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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