While the temporal integral of acceleration is velocity, and the second integral is position, it is very difficult in practice to use an accelerometer alone to find velocity and acceleration.

One might want to use an accelerometer, such as the one in a Wireless Dynamics Sensor System (WDSS), to find the velocity of a cart. The problem is that any offset error in the acceleration will cause the velocity calculation error to rise linearly with time. A position calculation will have error rising quadratically with time.

This means that no matter how carefully you zero a sensor, the calculation of position and velocity will eventually be unreliable.

Inertial navigation systems, such as those used on rockets and submarines, use additional information from other sensors and landmarks to correct the inevitable error that accumulates in time.

Simply integrating an accelerometer value will typically give poor values after several seconds.