Finding Relatively Accurate Velocity Using an IMU
Integration of acceleration to derive velocity is a difficult task.  This is the first step in dead reckoning.  Consider some of the following options to improve accuracy:

Some IMUs can be adjusted to increase sample speed. If the
acceleration is sudden, more samples my improve the accuracy of the
calculated velocity.
Try aligning just 1 of the axes of the IMU chip in the direction of
acceleration. Do this to simplify the problem.  Depending on the
Arduino you are using, the processor may not have the power to
perform the trig functions necessary for anything except
acceleration only along 1 of the IMU's axes.
Take care of loosing significant digits.  If using integers, try
multiplying everything up.  For example instead of 1 equaling 1
meter multiply the value up such that 1000 equals 1.000 meters.  Now
integer math can be used to calculate down to the mm.