anonymous
  • anonymous
How do i turn a growth function with respect to height with respect to time into acceleration with respect to time?
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
Differentiate it twice.
anonymous
  • anonymous
differentiate time?
anonymous
  • anonymous
wait distance / time :P

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anonymous
  • anonymous
Yeah differentiate the function with respect to time.
amistre64
  • 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
  • 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
  • anonymous
Well, I Have a huge problem regarding loggerpro...
anonymous
  • 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
  • anonymous
Now this is my raw data. (I've tired to make it exponential :P
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amistre64
  • amistre64
that looks like a bounded exponential
amistre64
  • amistre64
in other words, the data starts out looking linear, but there is a limit that it approaches
anonymous
  • anonymous
Yeah =/
anonymous
  • anonymous
Another picture, this is of my (initial) raw data and the Ln of height
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anonymous
  • anonymous
red = raw and blue = Ln(height)
anonymous
  • anonymous
ignore the first graph.
amistre64
  • amistre64
how did you obtain the data? what were the ...... ignore function activated :)
anonymous
  • anonymous
But still... do understand what I mean?
amistre64
  • amistre64
almost; can you show me the table that the data comes from? your experiment?
anonymous
  • anonymous
yeah 1 sec
anonymous
  • anonymous
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amistre64
  • amistre64
so did you come up with a good: y(s) = s function ?
amistre64
  • amistre64
the time taken to reach the meters? what does position have to do with time?
amistre64
  • amistre64
and of course the higher it gets the slower it goes :)
anonymous
  • anonymous
yeah umm 1 sec
amistre64
  • amistre64
i wrote a program that can fit this to a quadratic :)
anonymous
  • anonymous
i got y=0.5604x-0.8171
amistre64
  • amistre64
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anonymous
  • anonymous
Do you know how to expain it being a quadratic?
anonymous
  • anonymous
explain*
amistre64
  • amistre64
it would be a best fit line as well
amistre64
  • 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
  • anonymous
yeah, but the next question asks: How well do these functions fit your graphs? Are they a perfect fit? Explain your answer
anonymous
  • anonymous
What we are meant to do is determine the function for the graphs
amistre64
  • amistre64
perfect fit? any real life experiments are never gonna perfectly fit a model
anonymous
  • anonymous
There is one argument :)
amistre64
  • amistre64
models are ideals; real life experiments contain to many variables to account for
anonymous
  • anonymous
so how do i use this quadratic program?
amistre64
  • 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
  • amistre64
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amistre64
  • amistre64
another option is to do a method of 'least squares' which i forget the steps to :)
anonymous
  • anonymous
Alrighty, so ive got the quadratic: 0.807801462732185x^2 + -11.760157128268668x + 40.60929764207282
anonymous
  • 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
  • amistre64
i didnt see a table option for 'number of mentos'
amistre64
  • amistre64
and remember to use diet coke and the minty mentos....
anonymous
  • 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
  • anonymous
Heheh you're my last hope now :P
amistre64
  • amistre64
mythbusters did an episode on this menthos thing; try to check out their work :) get some ideas if you havent already
amistre64
  • 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
  • amistre64
that cut it short lol just google mythbusters mentos
anonymous
  • anonymous
No idea if this is allowed, but do you use skype?
amistre64
  • amistre64
aint got the periphials for it.....
anonymous
  • anonymous
I just want to screen share or something :L
amistre64
  • amistre64
do you know how to draw a vector field?
anonymous
  • anonymous
Nope.
amistre64
  • 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
  • amistre64
and watch it move :)
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amistre64
  • amistre64
they prolly have online stuff to do it quicker and easier tho
amistre64
  • amistre64
in fact, they proly have online best fit calculators too :)
anonymous
  • anonymous
O i can best bit in autograph, its just.. I need to beable to work it out manually. :C
amistre64
  • 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
  • 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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