about kinematics..pls help?

Question

a typical automobile has a maximum deceleration of about 7m/s^2, the typical reaction time to engage the brakes is 0.5s. a school board sets the speed limit in the school zone to meet the condition that all cars should be able to stop at a distance of 4 m.

a. what maximum speed should be allowed for a typical automobile?

b. what fraction of the 4 m is due to the reaction time?

Answer 1

s2 = v^2/(2*7)
s1 = 0.5v
s1 + s2 = 4
s2 = 4 - 0.5v
v^2 = 56 - 7v
v^2 + 7v - 56 = 0
v = (- 7 ± √(49 + 224))/2
v = (- 7 ± √273)/2
v ≈ (- 7 + 16.52271)/2
a.
v ≈ 4.761356 m/s ≈ 17 kph

b.
0.5*4.761356 = 2.38 m

Answer 2

we have 2 part in braking
1- reaction time : car go with initial speed . x1=v*t
that v: initial speed
t :reaction time=.5 s
x1: distance
2-braking : car decrease speed
(v2)^2-(v1)^2=2*a*x2
that
v2 :final speed=0
v1 :initial speed
a :acceleration=7 m/s^2
x2:distance

x1+x2=d=4
d=v1^2/(2*a)+v1*t