Re: University Physics

[Hugh Haskell <hhaskell@MINDSPRING.COM>]

At 12:47 -0700 9/24/02, Larry Woolf wrote:
> Headlights illuminate the road up to 160 ft in front of you.  If you are on
> a road with stop signs, what is the fastest speed you can drive and still
> stop safely at night?
> A typical reaction time for braking is 1.5 s (See Traffic Safety and the
> Driver by Leonard Evans) and a typical braking acceleration for a car is 17
> ft/s2.
This is certainly the same problem that Tina first posed, just
dressed up in PC clothing. But I suspect that there are a couple of
features of it that may make it somewhat less relevant than it
appears as first glance. First, at least in my benighted area, all of
the stop signs are done with ScotchLite, or some generic equivalent
(I'm sure MMM's patent has expired by now), which makes them visible
from substantially more than the "illuminated distance" (and many
cars now use halogen headlamps which have a range of more than the
"standard" headlamps). The 160 feet range would be more
characteristic of non-reflective objects, like animals (who aren't
looking at you), or pedestrians without proper reflective vests.

And second, the reaction time seems rather long to me. I have done
reaction time tests with my students over the years and they seem
able to achieve values of well less than .5 sec. I have also used the
little driving simulator that the driver's ed people use, and it has
a reaction timer, and I and the others who were using it the times I
played on one usually got reaction times of less than half a second
as well. This, of course, is not a systematic study, but it
represents more than just one data point. I suspect what is happening
in the quoted case is that it may be an average between reaction
times for "alert drivers" and "inattentive drivers." That is,
measuring the time between when the driver "should" have perceived a
problem, and when the brakes were applied. If this is the case, my a
priori guess would be that the distribution of times would be
bi-modal, with the "attentive drivers" clustered somewhere around .5
sec, and the "inattentive drivers" clustered somewhere higher than
1.5 sec. Thus the 1.5 sec may represent a false average (kind of like
the two statistician-snipers during a battle, who targeted the same
enemy soldier. One sniper's shot was wide to the left by 5 feet, the
other wide to the right by 5 feet, whereupon they confidently
reported success: "on the average, we got him!")--alert drivers will
typically do much better than average, inattentive drivers typically
much worse, so the 1.5 s figure really applies to nobody.

So I might modify Larry's problem to specify an alert driver, and
give a reaction time of .5 sec, then add a part (b) to specify an
inattentive driver with a reaction time of 2.5 sec. The difference in
safe speed for these two cases would be quite dramatic (somewhere
around 20 mph).

Hugh
--

Hugh Haskell
<mailto:haskell@ncssm.edu>
<mailto:hhaskell@mindspring.com>

(919) 467-7610

Let's face it. People use a Mac because they want to, Windows because they
have to..
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