Errr... I think I am doing a bad job of explaining something.
I'll use the car example, because it's familiar, despite the fact that it's a bad example. Just forget about traction, gears, brakes, etc. Forget about what your body can handle as well, we could just as easily be talking about an asteroid, a bullet, or a grain of sand - what the chunk of mass that you are dealing with is capable of withstanding doesn't apply.
So, take your car that is traveling 100mph in reverse, pop it into gear and apply acceleration forward. It doesn't have to be instant, just a gentle accel will do - even if it takes you an hour to go from -100mph to +100mph.
At the instant that you are at 0mph - freeze that snapshot. Your velocity at that point is zero. Your acceleration is still 200 mph^2 - you haven't let off the accelerator just because you came to a stop, as you can attest by trying this out in your car - though please use speeds MUCH slower than 100mph. You also need to ignore the fact that a car would usually decel using the brakes and then accel using the engine - which is why a car is a bad example.
Rocket engines are a better example - they get used in space, where there is little to no friction to worry about, and they can only provide positive thrust - no brakes in space.