How do you go from a position vs. time graph to a velocity vs. time graph?

[hexhall]

And visa versa. And I'm only in 9th grade, so please don't give me any complicated answers or links. I just want to know simple stuff like, "If there is a straight horizontal line in a velocity vs. time graph, how would that look like on a position vs. time graph?" Basically, I just want to know the rules like if you have a steep line on a velocity graph, how would that look like on a position vs. time graph. If you could list basic rules like this, that would help a lot. Also, if there were any links that helped, please feel free to post. Thanks!

 

[Hobin]

*scratches head* Do they teach basic calculus in high school? Do you live in the USA? My apologies for not having an immediate answer to your question. Well, I *do* have an answer. Multiple answers, in fact. I just don't know which one to give because I'm unfamiliar with the educational system in America.

 

[rcgldr]

How do you go from a position vs. time graph to a velocity vs. time graph?

The velocity versus time will equal the slope of the position versus time grapsh. The position versus time graph will equal the area below the velocity (to the x-axis) versus time graph.

So if velocity is contant, then position(time) = velocity x time.

 

[emailanmol]

(Note to other readers
This post is valid only for 9th grade physics)

Case 1:
You have a velocity vs time curve.You want the position vs time.

Area under the curve,(this will be fairly simple to grasp) will be the value of position.(x=v*t)

If the velocity curve is a straight line, the position is area of the triangle thus formed.


Vice-versa case


Look at this figure
http://en.m.wikipedia.org/wiki/File:Slope_picture.svg

Here y-axis is your position and x-axis is your time.

The value of (y2-y1)/(x2-x1)
Is your velocity

 

[hexhall]

Thank you emailanmol for making it a lot simpler. I have another question, if you could answer it. When you find the "area under the curve" do you kind of mean like the rise over the run, or change in y over change in x?

 

[emailanmol]

Hey,
I am glad I could help you.

Area under the curve is the area between the graph and x axis.

Read this article and it will be very clear.

http://www.physicsclassroom.com/class/1dkin/u1l4e.cfm

See the 3rd example of trapezium especially which will help you get full hold of what is required at your level :-)


See there is a simple principle for knowing what area gives you and what slope gives you

For eg:-
Lets take a v-t curve.

AREA under the curve is like calculating v*t, so it will give you displacement.

SLOPE is like calculating v/t which will give you acceleration.

So in general remember AREA under the curve gives you the quantity y*x where as SLOPE gives you y/x.(where y and x are quantities on y and x axis)

I hope I made it simple enough :-)

 

[hexhall]

Thanks emailanmol, you did really help a lot. I'm going to go into science class tomorrow, actually knowing what I'm doing. Also, thanks for the website too! See, I just got to this website (my norm was Yahoo! Answers) but physics really isn't...my best subject.

 

[emailanmol]

Hey,

Welcome to PF then :-)

Don't worry .Three years ago (when I was in 9th) even I coudn't realize how amazing a subject Physics is (Although I loved it all the way)


Over the course of these three years however, I have realized how interesting and
fascinating this subject actually is.
Its like perceiving the world and laws of nature in your own way , and understanding How stuffs actually work.


See, how much you love physics at 9th grade depends vastly on who teaches you and how he/she teaches you.
It also depends on how strong your Math is.It takes time to adapt, but believe me its worth the pain.(Also if you really love another subject, then carry on with it.Life is always about chasing your dreams :-) )

If you really want to make physics your subject and strengthen your concepts , I would recommend you buy (or download) Volume 1 of Resnick and Halliday and just read (just read at ninth grade) the first two chapters (and any other chapter which coincides with your chapters).
You will learn the same equatiobs of motion in a much more clear way and really have an edge on others :-)
(You can also read some of Feynman .If you feel its tougher at your level then you always have the option to stop.)

 

[hexhall]

Thank you so much for all of your help!