Get the mean of ball i.e from 15001x3 array at each time step...you will get 15001X3 means..i.e a single mean at each time step..and you said there are 15001 time steps.
Use diff and get difference of x,y,z of the mean. Divide this diff (dx,dy,dz) with diff of time i,e dt step. You have your velocity.
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