The speed limit in a school zone is 40 km/hr (11.1 m/s). A driver traveling at this speed sees a child run into the road 13 m ahead of his car. He applies the brakes at a uniform rate of -8.0 m/s2. The driver has a reaction time of 0.25 sec prior to stepping on the brake pedal.

Question

The speed limit in a school zone is 40 km/hr (11.1 m/s). A driver traveling at this speed sees a child run into the road 13 m ahead of his car. He applies the brakes at a uniform rate of -8.0 m/s2.  The driver has a reaction time of 0.25 sec prior to stepping on the brake pedal.
a. Determine the distance the driver travels during their reaction time
b. Will the driver hit the child? Yes or no. Show calculations to support your answer.

Anonymous · Accepted Answer

Vi = 11.1 m/s
v = 11.1 - 8 t
d = .25 *11.1 = 2.775 m during reaction time
now the brakes are on
v = 0 at what additional time?
8 t = 11.1
t = 1.39 seconds more
x during braking = average speed during stop * time
= 11.1 / 2 * 1.39 = 7.70 meters more
so stop distance = 2.775 + 7.70 = 10.47 meters total to stop
Whew, no problem :)