Car breaking speed physics priblem

[efofgee0508]

Problem: a typical automobile under hard braking loses speed at a rate of about 7m/s^2. the typical reaction time to engage the breaks is about 0.50 seconds. a school board sets the speed limit in a school zone to meet the condition that all cars should be allowed to stop in a distance of 4 meters
a)what maximum speed should be allowed for a typical automobile
b)what fraction of the 4 meters is due to the reaction time

any ideas?

 

[Astronuc]

Well one needs to look at the distance D traveled in the reaction time of 0.5 s, and in that time use distance = speed * time.

Then if something is traveling at speed V and is decelerating to a stop, then V² = 2ax, where x is the distance traveled for an initial velocity V with a deceleration of a.

So D is the distance traveled during the reaction time period and the total distance traveled is 4 m.

See - http://hyperphysics.phy-astr.gsu.edu/hbase/mot.html

Particularly
http://hyperphysics.phy-astr.gsu.edu/hbase/mot.html#mot1

http://hyperphysics.phy-astr.gsu.edu/hbase/mot.html#mot5