nojwod:
apparent acceceration may be a sensation or feeling not to be taken as a constant, but Thrust vs weight vsspeed vs distance ceratinly are fact.
And a very simple check which can be used as a gross error check is timing to speed.
30 seconds - 100 kts.
If after advancing the thrust levers and starting the clock at brake release this parameter is not met then it can be assumed something is incorrect,
ie not the correct thrust for weight, dragging brake, etc.
and it can then be taken that you may never reach V1 in the remaining distance.
Not to say if you reach 30 seconds and are not at 100 kts that you reject, but it is a guide, if you are at say 95 kts, accelerating, then the parameters have been met, but as in the MEL EK flt, they were so far beyond this from a timing point, that such a check would have been a huge wake up call.
why 100 Kts? have a look at brake energy charts, 100 kts is usually close to the top where wheels should stay intact at MTOW rejects.
Not to suggest this works for all types, but it seems to work quite well for most larger types. Boeing developed this very basic check over 40 years ago for the 747, and it is a great gross error check.