Solve the physics problem?

Question

A typical automobile under hard braking loses speed at a rate of about 7 m/s^2, the typical reaction time to engage the brakes is .50 s. A scheool board sets the speed limit in a school zone to meet the condition that all cars should be able to stop in a distance of 4m. What maximum speed should be allowed for a typical automobile? What fraction of the 4m is due to reaction time?

Answer 1

t(total)=t(reaction) + t(stop)
since the travel distace is known to be S=4 m and distance covered under acceleration is
S=.5at^2 +v(.5)

since S=4 we have

7t^2+v-4=0
and
v=4-7t^2

This problem can be solved iteratively.

t let t(braking )=1 sec

Then
S(total)=.5a t(braking ) ^2 + v t(reaction)
4=.5(7)(1)^2+v(.5)
Then v= 1m/s
Or v=3.6km/hour (that is about an average man walking speed)
We have to increase reaction distance :-)

Answer 2

This problem has two parts( the time of reaction and stopping time)
Distance total (Dtot)= Dist(reaction) + Dist(stop)
Dt = V0*t + (V0^2)/2a
4m = Vo.5s+ (Vo^2)/14
56m/s^2= Vo*7+(Vo^2)/14
Vo=4.76m/s
Dist reaction= 4.76m/s*.50s=2.38m
source volume 1 Physics for scientists and engineers ( Paul Tipler)