measuring the speed by integrate the acceleration

Hello !

I'm a student in France and I have a project : having the speed by integrate the acceleration. (sorry for my english !)

At first I wanted to by an accelerometer and an "inclinometer" to subtract the weight so I will only have the acceleration of my system. But I have found that the inclinometer are working with the projection of the acceleration of weight on the axis, so it only work if the inclinometer doesn't move, am I wrong ? My teacher said that it exists gyro-laser but it was way too expensive and may too big. But I've seen that it also exits simple gyroscope, I didn't really understand if it can give me the inclinaison of my system, if my system is moving. So I have only bought a MMA7361L accelerometer, do you know a composant that can give me the inclinaison when my system is moving ?

I bought a Arduino uno and a 1602 screen module (with all the connection furniture).

In my computer science course, we use python, so I've decide to study, the speed and precision of different method of integration, the rectangle one, the Trapezoidal rule, the Simpson's rule and Romberg's method. Do you know if i can find those algorithm wrote in the arduino language ? And do you know where I can find a algorithm for the screen module ?

thank you for reading and even more if you answer me ! Eliot

Ps if you want my python algorithm of integration i can give it !

This is a pretty good explanation of the difficulties you will encounter in your project (beware the numerical errors in the table):