MPU 6050 Accelerometer question

Hello everyone, I'm currently working with the MPU 6050 and im trying to get the velocity of the chip in the Z axis. The other two are easy (When I tilt the device in a certain direction these X and Y change) However, Z is different. When I look like a doofus and shake the device up and and down it seems to change (Not as much as the x and y.) What im just wondering (And because my time is short, I need this for a competition) if anyone has used this device to calculate the instantaneous velocity in the Z axis?

Or if anyone has any information on how I could accomplish this I would appreciate this. I assume I am going to have to use the gyroscope as well and do some trig to get the Z axis to cooperate, I am just unsure as to where to start

Thanks in advance!

You won't have much luck estimating velocity using an accelerometer. Read about why not here:

The reason Z seems different to you is that you have that axis pointing up or down. It is measuring g, the acceleration due to the Earth's gravity.