Question

Suppose a car is traveling at +15.0 m/s, and the driver sees a traffic light turn red. After 0.405 s has elapsed (the reaction time), the driver applies the brakes, and the car decelerates at 6.00 m/s2. What is the stopping distance of the car, as measured from the point where the driver first notices the red light

Answer 1

during 0.405 sec there is no acceleration;
therefore,
V=d/t
d=vt
d=(15)(0.405)

which is the distance car traveled before driver hits brake.

Now, a=-6 m/s^2 and car's final velocity vf=0. initial velocity vo=15 m/s

use
vf^2 = vo^2 +2as
to get s=distance traveled under acceleration.

s+d is your answer.