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Estimating variable velocity graphically

Assuming that you are able to create a plot of displacement versus time at closely-spaced points, you can estimate the variable velocity curve byconnecting each pair of points with a straight line and measuring the slope of each such straight line segment. An estimate of the velocity during the intervaldefined by a pair of points is the slope of the line that connects those points. The closer the points are, the better will be the estimate of thevelocity at a point half way between those two points.

In the situation where you are able to collect enough data to draw a smooth curve of displacement versus time, the instantaneous velocity at any point onthat curve is the slope of a line that is tangent to the curve at that point. Note, however, that the construction of such a tangent line is no small feat.

Units of velocity

If you recall your high school geometry course, you may remember that the slope of a line is given by the "rise over run." In other words, the slope ofthe line is the ratio of the height to the base of a right triangle for which the hypotenuse is on or parallel to the line.

Estimate some variable velocity values

At this point, I encourage you to use a straight edge, place it firmly against two pins that define a time interval on your graph board,estimate the slope of the edge, and record that slope as your estimate of the velocity at the center of that time interval.

Explanation of the code

The code in Listing 1 begins by declaring and initializing values to contain the parameters of the problem:

  • The acceleration of gravity in feet/sec^2. Note that this value is negative indicating that the gravitational attraction is toward the centerof the earth (down).
  • The initial velocity of the arrow in feet/sec. This value is positive because the direction of velocity is away from the center of the earth (up).
  • The height of the arrow when it is released, positive values meaning up from the ground.
  • The time interval at which successive estimates of the height of the arrow will be computed.

Working variables

Following that, the code in Listing 1 declares and initializes two working variables for time and distance that will change as the program progresses.

Then Listing 1 declares and initializes a variable named sp that is used solely to insert spaces between the columns in the output display.

A while loop

A while loop is used to evaluate the equation given earlier , to compute and display the height of the arrow every 0.25 seconds for as long as the arrow is above theground (height is positive). The loop continues to iterate and display time and height values in two separate columns (see Figure 4 ) until the computation produces one negative height value.

When the test at the top of the while loop determines that the previously-computed value for height was negative,

  • The body of the loop is skipped.
  • The "End Script" message is displayed.
  • The script terminates.

As you can see, this is not a complicated script in comparison with some of the scripts that were presented in earlier modules.

Questions & Answers

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
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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
Daniel
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
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
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
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
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.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
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Source:  OpenStax, Accessible physics concepts for blind students. OpenStax CNX. Oct 02, 2015 Download for free at https://legacy.cnx.org/content/col11294/1.36
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