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.

To brake or not to brake:
That is the question. 
-- with apologies to all of the Bard's living devotees.
wo 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. 
  • 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. 
  • 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 car, 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 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.
How much "sooner" and how much "later"?