I googled it. Reams of info on the subject. The op may want to do the same to find an answer to his specific question.
In my opinion, it is a very complex subject. Doppler shift, velocity computed in three dimensions...
As for measuring a quick move of a handheld gps, I suppose you could try it. My guess is that it will not be accurate, because that's not what it's designed for.
I think they use accelerometers for that type of motion.
I'm not a man of science, but I play one on the internet.