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Given the above, I would like to know if the interval's velocity would be equal to (S-Sx)/(new weight) + Sx.

My understanding of the difference between speed and velocity is that speed is measured from one interval to the next ignoring what occurs inbetween the measurements and velocity accounts for both speed and anything that has been lost during the speed interval.

I would like to know if my understanding is correct, and if not, then how it is not.

I also need to know when expanding squares such as, (x+y)^2 to x^2 + 2xy + y^2 if the 2 in the 2xy term should be expressed by another variable when dealing with velocity (1/0.5 = 2, but has intra-interval changes been ignored?).