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.
To brake or not to brake:
That is the question.
identical automobiles are traveling side-by-side at the same speed.
Both of their drivers observe a traffic signal change to red some distance
-- with apologies to all of the Bard's living devotees.
One driver takes his or her foot off the accelerator pedal
and begins to coast for as long as possible before applying brakes.
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.
Both eventually come to a stop at the signal side-by-side.
|At Point 0 in the sketch above, the cars are traveling
at v1 MPH.
The red car will arrive at its
destination sooner than the green car but
the green car will run out of gas later than
In red you see one car continuing
at v1 for tB1 seconds before applying its brakes
at Point 1.
Constant braking deceleration is shown for the red
which comes to a stop at Point 3 in a total of tB3 seconds.
Meanwhile, in green you see
the other car as it coasts for tC2 seconds, slowing gradually
to v2 in tC2 seconds.
Constant braking deceleration is shown for the green
car, bringing it to a stop at Point 3' in a total of tC3
How much "sooner" and how much