At 30 mph your braking time (the time between slamming the brakes on and you stopping) is 1.8 seconds. Reaction time varies, but depending on circumstances it usually is between half a second and a second.
At 55 we're already at well over 2.5s for braking alone, without reaction time.
Don't just pull numbers out of your ass.
1) The amount of energy at 55mph is roughly 5 times higher than at 30mph, given that brakes dissipate a fairly constant amount of energy at all speeds, that means your braking time at 55 is 5 times that at 30.
2) Thankfully, that doesn't mean your braking time at 55 is 9 seconds for an emergency stop. That's because your figure for 30mph is bullshit. The actual braking time for an emergency stop from 30mph is 0.8 seconds, and at 55, roughly 4 seconds.
All this put together means that when you're presented with a 4 second orange at 30mph, and you have to do an emergency stop, that basically means you fucked around for 2.8 seconds. That is, the 4 seconds is made up of 0.5 seconds of reaction time, 2.8 seconds of fucking around doing nothing at all, and then 0.8 seconds of actually stopping. As I said before - if you're failing to stop for a red when given a warning with an orange, you're driving dangerously.
Note, this can be observed in every day life. It's trivial to test, you approach some lights at the speed limit. When they turn orange, you start to gently brake for the lights. Observe that you come to a stop before the lights even turn red.