I have been recently told by a flight instructor that the normal engine response time from idle to go around thrust which is normally 6-8 sec increases when the aircraft is at or below vapp to approx. 14 sec.
BS
. The FAR requirement is 8 seconds - doesn't mention airspeed. Most modern aircraft (and anything currently produced by Boeing) has an "approach idle" setting that is automatically selected when landing flaps are selected (basically anything over flaps 20 for Boeing). Approach idle to go-around thrust will take less than 8 seconds regardless of airspeed (I've tested it on various Boeing aircraft sitting static on the ground - it usually takes about 6 seconds).