The school zone in front of your school has a posted speed limit of 25 mi/h, which is about 11 m/s. Let’s examine the stopping of a car in several different situations.
The driver is looking at her phone and has a total reaction time of 4.6 seconds as the car is moving at a constant speed of 11 m/s. If the driver slams on her brakes and slows down at a rate of -8.2 m/s^2, What is the stopping distance for the car in this situation?
a total reaction time of 4.6 seconds
I will assume this means the brakes get applied after 4.6 seconds
the car will have travelled 4.6 x 11 m/s before braking = 50.6 m
then xf = xo + vo t + 1/2 a t^2 and vf = vo + at
vf = 0 = 11 -8.2 (t) solve for t = 1.3415 seconds
xf = xo + vo t + 1/2 at^2
= 0 + 11 (1.3415) - 1/2 (8.2)(1.3415^2)
= 7.38 meters
7.38 + 50.6 = 57.98 meters