One can look at video of world champions in sport walking to find an upper estimate. What is normal man versus non-normal? There is a fuzzy border, so an answer will be never exact.

What part of body should have this speed? If body as a whole, then minimal observation duration should be one step.

I'm trying to simulate walking speed and I need to have an idea that how walking speed is changing over very short period of time (e.g., 0.02,0.1,0.2, and 0.5 sec). As I said, we know that average normal walking speed would be something around 0.5 to 1.5 m/s in controlled walking experiments. I just want to know how the speed is fluctuating. In other words, I need to know what is the maximum possible acceleration/deceleration over a short time period.

I think you can get an idea from your experiment data itself. You track people at each delta_t (0.02, 0.1, 0.2, 0.5 seconds) and draw the instantaneous speed (delta_s / delta_t) distributions for each of those delta_t. From these distributions you can get an idea about any upper/lower limits, average, stdev etc. 

Thank you Charitha for the response. Actually, our tracking accuracy was about 5-7 cm and if you calculate the displacements/speed for a very short period of time, you may not get accurate results. In previous studies, I was using 1 sec to calculate displacements and speed. I just wanted to see whether there are any studies that track the speed movements using more accurate devices.