Question

position vs time relationship

Answer 1

@amistre64

Answer 2

hye

Answer 3

hey*

Answer 4

displacement over time position over time same thing

Answer 5

yea i know i need to prove that position and time have a second order relationship by linearizing this graph i have of position vs time

Answer 6

so if u took a square root or squared a side to linearize the graph, would that prove its a second order relationship? if not then what is its relationship called?

Answer 7

@dareintheren

Answer 8

any idea if thats right?

Answer 9

this one?

Answer 10

yea i kinda asked it in the comments part a couple comments up

Answer 11

second order, are we talking about differential equations, or difference equations?

Answer 12

basically i have this position vs time graph and i have to figure out what relationship it shows. So i took the square root of the posion values and created a linearized version of the graph. does this prove it to be a 2nd order relationship? or what relationship is that?

Answer 13

can you post the graph?

Answer 14

i believe i could have also squared the time values to get a linearized graph but im not sure

Answer 15

yes give me one second

Answer 16

http://gyazo.com/7aec7b2a213c0c7dc426ccf7b1cd4d1d

Answer 17

that is position vs time

Answer 18

http://gyazo.com/e20d46f1eeb768f9e879e5e280729a6f

Answer 19

thats the linearized one i made

Answer 20

on the second graph i said it shows d is directly related to t^2, is that correct?

Answer 21

hmm, none of this rings any bells for me. so i don think i can be of much use with it.

Answer 22

well on the second graph would u say 2 would go in that little box?

Answer 23

second order to me implies that we can construct a differential or difference equation to model that data

Answer 24

at the moment, i couldnt even give an educated guess at what goes in the box

Answer 25

oh well i didnt know what to call the relationship between position in time in this graph

Answer 26

it may not be 2nd order relationship but i thought that might be what it was called

Answer 27

do we have the data points?

Answer 28

yes

Answer 29

http://gyazo.com/87884cbf2e86d338f9a08cc3528904a2

Answer 30

those are the points shown on the first graph

Answer 31

hmm, a second tier difference gives me 10 9 14, which is not constant, but if the data is from a real experiment, it is possible to define a quadratic regression line to give a best fit equation

Answer 32

it is from a real experiment

Answer 33

visually its a good fit to a quadratic equation

Answer 34

didnt i show that in the first graph i made?

Answer 35

but i was told we needed to linearize it and figure out what would go in that box wich i dont really get

Answer 36

there was no best fit equation shown in your post, so i wasnt sure how the curve was fitted to it

Answer 37

whats the alpha notation: \[d~\alpha~t^{[~]}\]

Answer 38

yea that is what i need to answer

Answer 39

i dont know how to read the notation that its written in

Answer 40

it means like d is proportinal to t^[]

Answer 41

to me, im thinking this:

if we linearize the best fit model, we take a derivative to get the slope of a line at any particular point, and apply it such that:
\[y=f'(a)(x-a)+f(a)\]

oh then, id say d is directly proportional to something like 5t^2 yes

Answer 42

y = kx tells us that y is directly proportional x

y = kx^2 ... proportional to x^2

Answer 43

so would u agree its a 2? i guess it is not called a second order relationship

Answer 44

you would just say t is directly related to t squared or something like that

Answer 45

keep in mind that i have never approached this subject so my assumptions could very well be null and void. but yes, i agree that its a 2 seems the most reasonable in my eyes.

Answer 46

ok, so to prove it with the graphs i made do u know how i could?

Answer 47

do i know how? no

my assumption is that the quadratic regression curve demonstrates that the data points fit well to such a proportion.

Answer 48

so do u think i could say that because taking the square root of the position created a linear line it shows the data demonstrates a quadratic regression curve?

Answer 49

pfft, that i got no idea about.

Answer 50

does that sound kind of right to you lol?

Answer 51

wish i could tell, but im not much of one for vernaculars :) im not sure if that is 'proof' or coincidence.

Answer 52

well i hope its right haha thank u so much though, u have helped me alot so far :D

Answer 53

goodluck with it all :)

Answer 54

:D