Stopping times are not actually that useful to us - we are normally more concerned about the stopping distance. Just as with times, the stopping distance is the total of two parts:
Whilst you are reacting to the hazard, the car is still moving! During your thinking time, you are not slowing down. We call the distance moved during this time the thinking distance.
With the brakes applied, the car slows down. The distance that the car moves whilst braking is called the braking distance.
Exam hint: it is vital not to muddle time and distance up! Thousands of pupils every year answer questions on this wrongly, even though they know what they mean.