That's an interesting question, and one that led
to considerable discussion around my lab. The
consensus, though, is that the teacher's
instruction has more to do with "common sense"
than with physics.
You're certainly correct
that driving speed doesn't change the mass of the
car, and that as long as the car is moving the
friction shouldn't depend on speed (otherwise
we're talking about the difference between kinetic
and static friction). What the effect comes down
to seems to simply be that a person has more
control over their car when they're driving more
slowly. If a strong gust of wind bumps you out of
your lane for even 1 second when you're traveling
65 mph, you travel 29meters in that second - quite
a long distance for your car to move in a place
you don't want it to be! If that same gust of
wind were to knock you off course for a second
while you were going 20 mph, you travel only9
meters - which feels a lot less scary while it's
happening. There maybe subtle effects going on
based on fluid dynamics, but these should
certainly be negligible for an object as massive
as a car. As far as us physicists can tell, the
effect you ask about seems to be based more in
common sense than in the mysteries of physics.
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