How do i turn a growth function with respect to height with respect to time into acceleration with respect to time?

- anonymous

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- anonymous

Differentiate it twice.

- anonymous

differentiate time?

- anonymous

wait distance / time :P

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- anonymous

Yeah differentiate the function with respect to time.

- amistre64

height is a position
derive it once to find the change in height with respect to time; which is speed, also known as velocity, or how fast the growth is.
derive again to find the change in velocity, which is acceleration.

- amistre64

derivatives are 'how something changes compared to something else'. Graphically, that represents slope right? how much does the y value change when you move the x?

- anonymous

Well, I Have a huge problem regarding loggerpro...

- anonymous

We did an experiment where we used mentos & coke in-order to investigate exponential growth patterns ect.. Now I'm struggling to realise why my raw data is linear and Ln data is exponential...

- anonymous

Now this is my raw data. (I've tired to make it exponential :P

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- amistre64

that looks like a bounded exponential

- amistre64

in other words, the data starts out looking linear, but there is a limit that it approaches

- anonymous

Yeah =/

- anonymous

Another picture, this is of my (initial) raw data and the Ln of height

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- anonymous

red = raw and blue = Ln(height)

- anonymous

ignore the first graph.

- amistre64

how did you obtain the data? what were the ...... ignore function activated :)

- anonymous

But still... do understand what I mean?

- amistre64

almost; can you show me the table that the data comes from? your experiment?

- anonymous

yeah 1 sec

- anonymous

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- amistre64

so did you come up with a good:
y(s) = s function ?

- amistre64

the time taken to reach the meters? what does position have to do with time?

- amistre64

and of course the higher it gets the slower it goes :)

- anonymous

yeah umm 1 sec

- amistre64

i wrote a program that can fit this to a quadratic :)

- anonymous

i got y=0.5604x-0.8171

- amistre64

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- anonymous

Do you know how to expain it being a quadratic?

- anonymous

explain*

- amistre64

it would be a best fit line as well

- amistre64

the most basic option would be to take the slope from one point to the next; table that up; and see what it looks like

- anonymous

yeah, but the next question asks: How well do these functions fit your graphs? Are they a perfect fit? Explain your answer

- anonymous

What we are meant to do is determine the function for the graphs

- amistre64

perfect fit? any real life experiments are never gonna perfectly fit a model

- anonymous

There is one argument :)

- amistre64

models are ideals; real life experiments contain to many variables to account for

- anonymous

so how do i use this quadratic program?

- amistre64

you plug in three data points and it takes them to figure out the quadratic that bends to those points; then to test for accuracy, I used a feature to put in a random 'x' point to see if the quadratic is good enough

- amistre64

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- amistre64

another option is to do a method of 'least squares' which i forget the steps to :)

- anonymous

Alrighty, so ive got the quadratic: 0.807801462732185x^2 + -11.760157128268668x + 40.60929764207282

- anonymous

cause what I have to do is work out the equations for each graph, preferable manually.. then predict the spray for 5 mentos.. Justify your response in mathematical reasoning..

- amistre64

i didnt see a table option for 'number of mentos'

- amistre64

and remember to use diet coke and the minty mentos....

- anonymous

We have already conducted the experiment its just if i were able to work out 1 i'd be able to do the others :) However, for number of mentos there is one for 4/7/9

- anonymous

Heheh you're my last hope now :P

- amistre64

mythbusters did an episode on this menthos thing; try to check out their work :) get some ideas if you havent already

- amistre64

http://www.google.com/search?q=mythbusters+mentos&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a

- amistre64

that cut it short lol
just google mythbusters mentos

- anonymous

No idea if this is allowed, but do you use skype?

- amistre64

aint got the periphials for it.....

- anonymous

I just want to screen share or something :L

- amistre64

do you know how to draw a vector field?

- anonymous

Nope.

- amistre64

you strat out with something like this; and for each point you find the slope (y/x) and plug a vector representation of it at the point to see where the data is moving

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- amistre64

and watch it move :)

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- amistre64

they prolly have online stuff to do it quicker and easier tho

- amistre64

in fact, they proly have online best fit calculators too :)

- anonymous

O i can best bit in autograph, its just.. I need to beable to work it out manually. :C

- amistre64

manually can be a pain; especially with alot of data points and decimals involved; that reason we have computers is to use as a tool to help us; it aint a cheat ya know :)

- amistre64

they teach you the manually so that you have the concept of why it works and how to get to an answer when you aint got the tools avaiable; but before computers it took alot of good mena dnwomen and a few good trout many years to do a single math problem

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