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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

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
I'm not sure why it wrote it the other way
I got X =-6
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
Idrissa Reply
im all ears I need to learn
right! what he said ⤴⤴⤴
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
I'm not good at math so would you help me
what is the problem that i will help you to self with?
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele 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, 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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