To
Brake or Not to Brake
Inspired by Brakes
in A Certain Bicyclist:
An off-beat guide to the Post-Petroleum Age.
Copyright ©2006 by Paul Niquette.
All rights reserved.
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To brake or not to brake:
That is the question.
-- with apologies to all of the Bard's living devotees.
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identical automobiles are traveling side-by-side at the same speed.
Both of their drivers observe a traffic signal change to red some distance
ahead.
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One driver takes his or her foot off the accelerator pedal
and begins to coast for as long as possible before applying brakes.
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The other driver continues with his or her foot on the accelerator,
maintaining a constant speed until the last possible moment before applying
his or her brakes.
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Both eventually come to a stop at the signal side-by-side.
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At Point 0 in the sketch above, the cars are traveling
at v1 MPH.
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In red you see one car continuing
at v1 for tB1 seconds before applying its brakes
at Point 1.
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Constant braking deceleration is shown for the red
car,
which comes to a stop at Point 3 in a total of tB3 seconds.
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Meanwhile, in green you see
the other car as it coasts for tC2 seconds, slowing gradually
to v2 in tC2 seconds.
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Constant braking deceleration is shown for the green
car, bringing it to a stop at Point 3' in a total of tC3
seconds.
The red car will arrive at its
destination sooner than the green car but
the green car will run out of gas later than
red
car. |
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How much "sooner" and how much
"later"?
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