In Reply to: No, that is not correct. posted by Rudy on October 07, 1999 at 10:41:43:
: The two second rule would work only if the car ahead could somehow come to a dead stop instantaneously.
Actually, the two second rule takes into account exactly what you described. If an immovable object suddenly appeared exactly two second's distance in front of the average US driver there would absolutely be a collision. The two second rule works on the fact that rates of change can not approach infinity (IE: instantaneous stop). The two seconds is mostly for actual driver reaction time.
Then you've got the case where you're following at two second's distance (any speed), the car in front of you slams on the brakes, and you have nowhere else to go. Assuming your car has aproximately the same braking qualities (stopping distance, etc) you have 2 seconds to realize what happened and take action. The longer you take to react, the closer you will continue to get to the vehicle in front of you until you come to a complete stop. Unless the brakes are applied on your car at precisely the same time they are applied to the car in front, you will always be moving faster than the car in front until you completely stop and you will continue to close in. Even if you (and your car) can decelerate at a higher rate than the vehicle in front of you at best you'll be calling it awfully close if you have a fast enough reaction time. This equation gets very complicated since it involves: delta of times of initial application of brakes of each car ; delta in initial vehicle speeds ; deceleration rates of both vehicles ; distance between vehicles ; and initial speed of each vehicle (or absolute time for complete deceleration of each vehicle)
You're making assumptions that you really shouldn't be. In you're example you state that your closing rate is only 20 MPH and that you still have "a long time to apply brakes". You are absolutely correct if the lead vehicle does not continue braking. If we make the assumption that deceleration rates are linear (though they most certainly are NOT) and use your example:
1) both cars at 60MPH with 2 second distance between
2) lead car brakes from 60-40 in 2 seconds
3) trailing car applies brakes at the end of this two seconds.
4) Both cars experience identical deceleration rates
5) 4 seconds later lead car comes to a complete stop and trailing car is still moving forward at 20 MPH
6) trailing car is where?
Lets see what happens:
Time separation lead speed trail speed
===== ========== ========== ===========
0 176 ft 88 ft/sec 88 ft/sec
2 sec 117.3 ft 58.7 ft/sec 88 ft/sec
4 sec 58.6 ft 29.3 ft/sec 58.7 ft/sec
6 sec 0 ft 0 ft.sec 29.3 ft/sec
Hmm. The trailing car is still moving forward, the lead car has stopped, and there is no distance between them. Sounds like a collision to me (at 20 MPH).
In fact, if you use ANY distance and take that entire distance to react you WILL have a collision. You need to use the same points of reference in your calculations and follow the event to completion. What you said sounds good but just isn't the case.
It is actually funny your choice of examples. This was almost exactly an example from my first semester ME class (far too long ago :-)) and it surprised a large number of people then as well.