[magnets]

You are correct, you can take the integral of acceleration to get your changes in velocity, but the sensor is not really accurate enough to get a reliable velocity. The accuracy of your current velocity depends on how accurate you were a second ago, which depends on how accurate you were before that....

Just like when you integrate the angular rate given by a gyro, and drift is present over long periods of time, your velocity will drift, but a lot more. Getting an encoder on the shaft is one way to measure velocity, but they can be hard to work in if you've already started designing.

You can use an optical sensor and paint half a shaft white and the other half black, and measure velocity based of the frequency of the change from white to black.