How to get a smooth velocity and acceleration from pixel offset

I'm working on a movable sensor which tracks(follows) flying objects. I do simple image processing at particular frame interval(dt=40ms) and during that time I find the distance(dx) of objet from centre and calculate velocity( v= dx/dt) and acceleration(a=dv/dt) and give command of a,v to the moving platform.

But I found difficulties to calculate velocity due to noise, it gives erroneous values. The object I'm tracking has a path mostly parabolic/ linear but very high speed. To smooth this velocity I used cubic B spline but no notable improvement..

Any suggestions.