The panic response is very difficult to overcome.
However, some people will try to apply the brakes gradually (as you would when coming to a stop normally). And in that case the brakes won't respond as one might expect. If the brakes don't seem to work, push harder until they do.
EDIT: Reading a comment farther down, I'm reminded that this is a matter of the copper pads getting too hot rather than wearing away. Same effect though.
Logically, all I needed to do was take a deep breath and move my foot sideways, but all I could think about was pulling up, which of course only exacerbated the problem.
It's not easy to think rationally when you are driving a car with several people accelerating when it should be breaking...and in the case of the linked story, it's not easy to accept blame either.
- Shut off the engine
- Put it in neutral
- Stand on the brakes (all but the most souped-up aftermarket monsters will have brakes that are stronger than the engine. Please note, STAND ON THEM. If you drag them lightly, you run a higher risk of overheating them, rendering them useless)
- Use the emergency brake
- Use the clutch (if it's a stick)
- Pull all large fuses from fuse box
- Induce a spin
- Drive the side of the car into something like a divider to scrub speed
- Run into the back of another car traveling close to your speed. They will likely slow down, slowing you down.
In short, there's a whole lot of things you can try. People just don't always know very much about driving/cars, or don't think well while panicking.
When it happened to me, I was in a parking lot. The pedal was accidentally pushed past a fold in the floor mat, which caught it and pushed it down. I was hurtling toward the curb in a small parking lot -- the car was a Mitsubishi 3000GT VR-4. It was scary. Very scary. Even knowing it was a stick shift, and all I had to do was press the clutch and listen to my poor engine ping the rev limiter while I figured out what happened.
I can imagine a lot of circumstances where this would be worse. Imagine if it happened in a school zone, unexpectedly. Imagine if it happened while you were parking.
I think that's part of the reason that we haven't really heard as much about it -- we hear about the catastrophic ones, or the higher profile ones, but the majority of cases probably weren't dire.
About to hit something unexpectedly->slam foot down on wrong pedal->omg the car accelerated when it should have stopped!