linear X,Y,Z with respect to world coordinate

Hi All,

I would like to use MPU-6050 in my application and I need to compute the linear X,Y and Z with respect to the world coordinate ( from the starting point of the sensor in motion).

a. How to compute the linear X,Y and Z with respect to world coordinate?
b. What will be the accuracy of X,Y and Z?
c. Is it better to use Quaternion? if yes how to do the transformation? Do we have any reference code for the linear X,Y,Z computation?
d. what rate we can compute the X,Y,Z using MPU-6050?

Please share your expertise on this.

Thanks & regards,
Krishna