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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

how can chip be made from sand
Eke Reply
is this allso about nanoscale material
are nano particles real
Missy Reply
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
where is the latest information on a no technology how can I find it
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
has a lot of application modern world
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
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
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
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 .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
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
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Harold walks to school by walking 600 m Northeast and then 500 m N 40∘ W. Determine his resultant displacement by using accurate scale drawings.
Lethabo Reply
Draw a frame of reference with house A as the origin and write down the positions of houses B, C, D and E.
jason 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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