Leadfoot Lou enters the Rest-to-Rest auto competition, in
Chapter , Problem 101(choose chapter or problem)
Leadfoot Lou enters the Rest-to-Rest auto competition, in which each contestants car begins and ends at rest, covering a fixed distance L in as short a time as possible. The intention is to demonstrate driving skills, and to find which car is the best at the total combination of speeding up and slowing down. The course is designed so that maximum speeds of the cars are never reached. (a) If Lous car maintains an acceleration (magnitude) of a during speedup, and maintains a deceleration (magnitude) of 2a during braking, at what fraction of L should Lou move his foot from the gas pedal to the brake? (b) What fraction of the total time for the trip has elapsed at that point? (c) What is the fastest speed Lous car ever reaches? Neglect Lous reaction time, and answer in terms of a and L.
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