Question

Acceleration graph help

Answer 1

what do you need help with?

Answer 2

What can be found using this graph? Could I integrate and find velocity?

Answer 3

by numerical methods most likely since i dont see a rule for it

Answer 4

This graph is from a rollercoaster, we have an assignment to analyse the graphs. I'm not sure what I can work out by using the graph.

Answer 5

average velocity in a given interval .. stuff like that comes to mind

Answer 6

Yeah I was thinking about that, how would I work that out?

Answer 7

I can use integrals if possible

Answer 8

since there is no rule for mathing it up; youd have to consider numerical methods that are approximations

Answer 9

You cant take an integral per say because you do not have an equation.

Answer 10

simpsons rule; trap rule, other ruley type rules

Answer 11

hmm okay

Answer 12

I know you can get an average velocity over an interval by taking the area under the curve and dividing by the interval.

Answer 13

where the graph is under the line we know it is slowing down

Answer 14

Anytime the graph crosses the x-axis the velocity should be 0 I believe.

Answer 15

Yeah, I only need the average velocity of the largest peak. And the graph is pretty out of place, the graph should start at 0, but it starts at 10m/s^2

Answer 16

the height of the curve tells us how fast the velocity is changing; since acceleration is the derivative or slope of velocity

Answer 17

tis is definantly a computer aided project

Answer 18

Well I do not think you can get an exact without having a equation to go off of but I would calculate the area as if it were a triangle seeing as that it is pretty close maybe?

Answer 19

How can I find the area under the peak from t=40 to t=45?

Answer 20

I think the average velocity of the tallest peak would be about 20 m/s.

Answer 21

The tallest peak reaches 42. So I used that as the height over the interval 42sec till 44.5 sec

Answer 22

From 40 - 45 it should be about 25 m/s

Answer 23

but spykes said the graph is not centered properly
it should oscillate about a=0, correct?

Answer 24

yeah

Answer 25

O well crap those numbers are off then.

Answer 26

yep :/

Answer 27

in any event, Simpsons rule is going to be a much better approximation than trapezoids, but you will need /very/ small intervals
so I'd say it's just not practical without computer aid

Answer 28

Could you explain how I would use Simpson's Rule if it's not too much hassle?

Answer 29

it's like trapezoidal rule, only with quadratic-shaped pieces
do you know the trapezoidal rule, or any Reimann sum?

Answer 30

I've heard of it, but I think we only briefly went over it

Answer 31

If you don't know any Reimann summing techniques I'm afraid Simpson's rule is not possible to explain
Here is a good link on the most basic Reimann sums
http://tutorial.math.lamar.edu/Classes/CalcI/AreaProblem.aspx
and here is one for Simpson's Rule
http://tutorial.math.lamar.edu/Classes/CalcII/ApproximatingDefIntegrals.aspx

I could try to explain the idea of the Reimann sum, but... it's kinda tricky

Answer 32

Alright, I'll have a look. Thank you

Answer 33

Sure, why don't you read it and if a particular part troubles you, ask?
that way I can help you more efficiently

Answer 34

simpsons; use the end points and the midpoint of the interval to form a parabola with that matches the curve better

Answer 35

spose we have 3 points of interest; (a,s)(b,t)(c,r)

\[RREF\begin{pmatrix}
a^2&a&1&s\\
b^2&b&1&t\\
c^2&c&1&rs\\
\end{pmatrix}\]
should get us the coeffs of a suitable parabola to fit the curve at those points

Answer 36

not rs, thats a typo lol

Answer 37

Ah yes, I remember doing the basic Reimann problems in class

Answer 38

Thanks for trying guys, I'll just skip it and ask about it in class.