What could be causing the RPM in my car to be bouncing around when accelerating.?

If the car is accelerating smoothly (no misfire/jerking/chugging) but the tachometer needle bounces all over the place then the problem is almost certainly with the ignition coil. The ignition coil ramps up the voltage to fire the spark plugs when the current to the primary coil is shut off and the voltage is induced into the secondary coil to fire the plugs. The tachometer is a display gauge that monitors how many times the coil fires the plugs and calculates engine speed from that input. if there is an internal short circuit in the coil the coil will "break down" and the result is the tachometer needle bounces all around because the coil input signal is erratic.

you may or may not feel the effects of the coil breaking down. in sever cases the engine misfires because the internal short circuit doesn't allow full voltage to build before the plugs are fired. In other cases, the short is not evident because there is still a high enough voltage being delivered to the plugs.

replacing the ignition coil is the usual fix. there is the rare occurance where the tachometer is bad but that is very, very unusual. Coil failures on those year cars however are one of the most common things that occur.

hope that helps

If it's bouncing from 3000 to 8000, it's not a true indication of the RPM since your motor would be blown, and no fuel problem or anything else would make it vary 5000RPM! It's prob the engine speed sensor, not sure what kind is in a 92 Accord.

That sounds like a misfire. Change the spark plugs. Be careful to not mix up the wires- do them one at a time. Make sure the gap is correct before you put each sparkplug in.

your injectors could be clogged or the gas could have gone bad