# Homework Help: Integration error

1. Jul 28, 2010

### mark2468

Hi.

I have a set of data representing acceleration. To get the distance I integrate twice using a summation method and looks like:

accelleration: 0, 40, 30, -50,-80, -40.
velocity: 0, 40, 70, 20, -60, -100.
distance: 0, 40, 110, 130, 70, -30.

The distance should be zero as the movement goes back to the original point so there clearly is an error. Is there a better way to get the distance. I have heard runge kutta is good for this sort of stuff but am not sure where and how to put the data in. Any suggestions to how i can sort out this error.

Thanks.

Mark.

2. Jul 28, 2010

### Staff: Mentor

Can you include time information in your dataset? What are the time intervals?

3. Jul 28, 2010

### mark2468

time intervals are 0.333 seconds.

4. Jul 28, 2010

### Staff: Mentor

If your acceleration is 40m/s^2 for 1/3 of a second, you are not going 40m/s at the end of that time interval....

5. Jul 28, 2010

### Strants

And is the acceleration in units per second^2? If so, haven't you got the wrong values for velocity, as the time intervals were less than a second?

EDIT: missed berkeman's post, sorry

6. Jul 28, 2010

### ehild

Apart from the length of the time interval, the displacement during a time interval Δt is the average velocity multiplied by Δt. In the first interval it is 20 (Δt)2, and the total displacement is the sum of all the individual displacements.

ehild

7. Jul 28, 2010

### mark2468

So what is the best way to synchronise them. Is there a formula or just divide by that ammout. e.g. 40/3, 30/3 etc or whatever the sample interval is. Any links with examples of this available?

Thanks again.

8. Jul 30, 2010

### ehild

Assuming constant acceleration during a time interval Δt, the displacement during Δt is

d=(v(initial)+v(final))/2 *Δt.

ehild