Question

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

Answer 1

Differentiate it twice.

Answer 2

differentiate time?

Answer 3

wait distance / time :P

Answer 4

Yeah differentiate the function with respect to time.

Answer 5

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.

Answer 6

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?

Answer 7

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

Answer 8

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...

Answer 9

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

Answer 10

that looks like a bounded exponential

Answer 11

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

Answer 12

Yeah =/

Answer 13

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

Answer 14

red = raw and blue = Ln(height)

Answer 15

ignore the first graph.

Answer 16

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

Answer 17

But still... do understand what I mean?

Answer 18

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

Answer 19

yeah 1 sec

Answer 20

so did you come up with a good:

y(s) = s function ?

Answer 21

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

Answer 22

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

Answer 23

yeah umm 1 sec

Answer 24

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

Answer 25

i got y=0.5604x-0.8171

Answer 26

Do you know how to expain it being a quadratic?

Answer 27

explain*

Answer 28

it would be a best fit line as well

Answer 29

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

Answer 30

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

Answer 31

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

Answer 32

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

Answer 33

There is one argument :)

Answer 34

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

Answer 35

so how do i use this quadratic program?

Answer 36

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

Answer 37

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

Answer 38

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

Answer 39

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..

Answer 40

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

Answer 41

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

Answer 42

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

Answer 43

Heheh you're my last hope now :P

Answer 44

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

Answer 45

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

Answer 46

that cut it short lol

just google mythbusters mentos

Answer 47

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

Answer 48

aint got the periphials for it.....

Answer 49

I just want to screen share or something :L

Answer 50

do you know how to draw a vector field?

Answer 51

Nope.

Answer 52

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

Answer 53

and watch it move :)

Answer 54

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

Answer 55

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

Answer 56

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

Answer 57

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 :)

Answer 58

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