What is the formula for calculating distance from acceleration data?

[parmeet]

Homework Statement [/b]

I have a device which gives me acceleration at any desired interval. So let's say i set the interval as 10ms and start moving the device from initial velocity 0. I will get readings for acceleration every 10ms. Using this data i want to calculate the distance which the device has travelled. Can anyone give me a formula for this?

 

[NobodySpecial]

In theory it's simple acceleration is speed/time
So if you started at 0m/s and 10ms later were doing 1 m/s then the average speed during that time interval is (1.0 - 0.0)/2 = 0.5m/s and since distance is speed * time you traveled 0.5m/s * 10/1000 s = 0.005m
If you then have a reading of 0 you are still traveling at the 1m/s speed and so every 10ms you move a further 1.0 * 10/1000 = 0.01m

The problem is that in reality the noise from the sensor will be much larger than the acceleration so you need all sorts of complex averaging to get a sensible answer - look up "Kalman filter"