You are driving down a straight highway at 20 m/s (72 km/h) on a foggy night. Suddenly you see a truck stopped directly in front of you a distance d down the roadway. Will you be able to stop in time?
Assume that your reaction time is 1.0 s and that when you step on the brake you can achieve a maximum deceleration of 4 m/s2.
(a) What distance will you have travelled after 1 s? After 2 s?
(b) What is the shortest distance d that will allow you to stop before hitting the truck?
(c) Suppose the truck is only 52 m away when you first see it. What will your speed be when you collide?
(d) If you had better brakes you would be able to stop within 40 m. What would be the smallest deceleration in order to stop before hitting the truck in this case?
(e) Suppose the truck is only 15 m away when you see it. Is there any value of braking deceleration that would allow you to avoid collision after your 1 s reaction time?