In Reply to: Still missing a point posted by Long Distance on October 07, 1999 at 13:57:46:
If the car in front of you blows up unexpectedly and sends shrapnel backwards at 100mph, you will collide with that shrapnel regardless of your speed. You can make up any kind of situations you want where you can get in trouble.
But lets look at what I was talking about:
Well lit, clear, sparsely populated (with cars) highway. Roughly one car every two seconds of separation (counting all three lanes). What would cause someone to panic stop in such a case? Short of a nuclear explosion, alien landing, plane crash etc... very few things. I have actually never see anyone panic stop on a highway in these kinds of situation.
What could happen is that the guys sees a cop, a dog runs out (not very likely on big highway - but could happen), he suddenly realizes he is going the wrong way and hits the brakes as some idiots are prone to do. In all of these cases he will shed speed quickly but will not stop. Now if he has a sudden reason to stop, such as the aforementioned cataclysmic phenomenons, you are likely to see them at the same time as he is.
Secondly, I picked 2 seconds reaction time because I was playing devil's advocate. My reaction time is probably on the order of 1/2 second (if I do not see the 'reason to slow down' before he does which is usually what happens) and with my better than average brakes I can probably out-brake him just from that standpoint (I do not ride on Porsches' or Ferraris' bumpers either).
Combine this with the fact that I will likely only slow down a little (20mph or so and you can see that there is very low risk.
Lets do your math more realistically:
0 176ft 88ft/s 88ft/s
.5 174.2ft 80.666ft/s 88ft/s
2 163.25ft 58.7ft/s 66ft/s
2.5 161.4ft 58.7ft/s 58.7ft/s
For a total closed distance of 14.6ft out of 176ft. I don't know about you but that isn't exactly hair raising for me. And I assumed same braking rates.
By the way, using real math your example comes to:
0 176ft 88 ft/sec 88 ft/sec
2 146.7ft 58.7ft/s 88ft/s
4 88ft 29.3ft/s 58.7ft/s
6 29.3ft 0ft/s 29.3ft/s
8 0ft 0ft/s 0ft/s
So there actually is an impact at 0mph. You have to remember that your speed for a two second interval which starts at 60mph and ends at 40mph with constant decelaration is 50mph not 40mph...
Well, I hope I didn't bore you to death.