A motorcycle with street tires on it will never out stop or out turn a car, the only safety valve you have is the throttle. Braking means nothing, I never have to brake hard on the street. I leave that riding for the track. I ride in shorts, flip flops and shades, that's it. If I have to brake hard, I screwed up. I do typically find 2 situations per ride where I need a good bit of throttle. I like riding without all the gear (as I've been doing since around 8 or so...) so I pay very close attention to what goes on well out in front of me. How far I can see dictates how fast I ride. The wild card is the guy between 4:30 and 7:30 that can get me. It's typically the guy shooting down the on ramp straight into the left lane, or the guy (or gal for that matter) pressing their car through traffic at 20-30mph above the common rate of traffic dropping in from the left. Those are the typical people who have tried to kill me without even seeing me (yes, loud pipes save lives, I wish someone would make a muffler with an "off" switch) and they are what I rate as the most hazardous thing to me. Typically they are 1.5 seconds away from impacting me by the time they first come into view. That's when big bikes shine, because I just turn the "go" handle and get from 60-100 and put 2 cars between me and them in less than that 1.5 seconds. I rarely pull over a 1/3rd of a g stopping, I've barked tires accelerating though. I have in racing applications though applied brake heavily, I've even f-d it up and highsided, but then, I have the gear for that and it's a whole different thing. What kinda ticks me off is the Walter Middy sport bike riders (and I've had sport bikes forever, even had an RG-500 Gamma back in the day) who treat the street as if they were in some kind of "Fast and Furious" movie. Movies are movies, they're not reality. Wanna play at the ends of the performance envelope, race locally. Doing it on the street just breeds ill will to all motorcyclists. You scare people, and scared people get mad.
BTW, I've never seen 2 gs out of a motorcycle except 1 and that was back in the day when they had Fuel Bike classes, those were insane and so was my buddy. There is no bike on the street that can pull over 2gs in any direction. Perhaps that car you were stopping next to was still rolling when you hit the brakes.