That sounds like a really interesting project.
Not sure if you'll be able to get the required information without a gyro, but no matter - I seek to set you
on the path of converting the acceleration data into movement or displacement data.
Basically, when we move, we can calculate the distance travelled by multiplying the velocity with the time.
So, 10 meters/second for 10 seconds = 100 meters
Trouble is though, the sensor provides G values - or acceleration as compared to the magnitude of gravity.
So, you need to work out the speed at any one time before you can convert this to a distance. This involves (yet more)
There's a description of the relationships between the various quantities needed, here: http://en.wikipedia.org/wiki/Classical_mechanics#Position_and_its_derivatives
I saw a discussion that looked at integrating (calculus term) the acceleration values over time to give positional data.
From memory, it was in a discussion about DIY SegWay self-balancing, type robots. You'll probably find some joy
in that type of a setting/forum.