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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

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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