What is the stopping distance of the car as measured from the point where the driver notices the red light?

Question

The question is:
Suppose a car is traveling at 20 m/s and the driver see's a traffic light turn red. After .530 seconds has elapsed (the reaction time) the driver appiles the breaks and the car decelerates at 7.00m/s^2. What is the stopping distance of the car as measured from the point where the driver notices the red light?


Please explain the formula's used to arrive at the answer. Thank you.

Answer 1

Distance Formula:
d=Vo*t+0.5a*t^2

The total distance travelled will be the distance travelled
during the 0.53 seconds of reaction time at the full
20 m/s velocity plus the distance travelled during the
breaking time. Therefore, use two separate distance
formulas added together for the total. The deceleration
time will be obtained from average time to stop from
20 m/s with 7 m/s^2

Net velocity formula(find the time when net velocity is 0):
v=v-at
0=20-7t
7t=20
t=20/7
=2.857 seconds

dt=d1+d2

dt=[20*0.53] + [20*2.857-0.5*7*2.857^2]
=39.171 meters

Answer 2

Two formulas
1. The distance traveled at constant speed in the 0.530 seconds at 20 m/s
2. The distance traveled in slowing down 0 = 20 m/s - T*7.00 m/s^2 solve for time then for distance.
Add the two distances together.