Essentially, instantaneous acceleration is just noise - the true number is the average value over a period of time that is related to the study - are we looking at a rocket taking off, a runner in the starting blocks, or the temperature of an atom?

I think a good way of looking at this issue is to go back to the early days of RADAR speed detectors - the first generation were considered to be unreliable and often booked people for speeding when they claimed that they were not speeding. After a year or two the problem was found to be that the RADAR guns reported the highest speed - essentially measured in terms the the highest frequency returned by the RADAR echo from the vehicle. This could be much higher than the vehicle speed if a headlight or some mechanical part of the front of the vehicle was shaking backwards and forwards ... when it moved forward it generated an instantaneous signal that was faster than the actual speed of the car ... "Book em Danno"