What should be happening in this situation is clear... A 'thinks bubble'... 'Hey... why are we accelerating so slowly? Why is the runway end coming up? Mmmm, something is not right...
Reaction... before, or certainly past V1, we are now going flying. Lets apply full-power, manually (Firewall the trust levers) and get this aircraft into the air and climbing away. Sort out/discuss the cause later.
By coincidence an accurate description of what happened to me one night take off. . Actual event at night. A Pacific atoll runway 5600 ft long with the ocean at end of runway. B737-200. Planned 2.18 EPR with associated 101% N1. I was dead heading in the jump seat.
F/O was PM and captain set thrust levers to 2.18 EPR. Cockpit lighting dim due night. The difference between 101%N1 and 90% N1 on the needles was about 3mm and easily missed especially as both pilots were concentrating on the take off run and no visible horizon. All other engine instruments were parallel and in the needle positions where expected.
It was not possible to gauge exact rate of acceleration at night by seat of pants feeling. With about five runway lights to go, it became evident we were not going to get airborne by the end of the runway. The captain immediately took control, simultaneously fire-walled both engines and hauled back on the control column at what was then V1 minus 15 knots.
It was then an immediate kick in the back increase in thrust was felt. The FDR later showed we maintained 20 feet over the water for half a mile and before climbing even though the body angle was 15 degrees up. The high body angle caused the engines to blow ground debris back over the runway. . On fire-walling the engines the EPR shot up to 2.25 an unheard of figure in the JT8D-17 engines.
On setting 1.98 EPR eventually after flap retract, the rate of climb was significantly less than scheduled. Comparison between 1.98 EPR and expected N1 showed the N1 was down by 10%. The decision was made by the captain to return to land. Investigation revealed that both PT2 probes were blocked thus giving an erroneous EPR reading to the crew. In fact at 2.18 indicated EPR we actually got about 90%N1 instead of the planned 101% N1.
The point being made that it is difficult to accurately predict the rate of acceleration in airspeed between 101% N1 and 90%N1 until it may be too late with the end of the runway coming up fast - especially with lack of cues at night.