A motorcyclist travels around a curved path that has a radius of 400 feet. While

Question

A motorcyclist travels around a curved path that has a radius of 400 feet. While traveling around the curved path, the motorcyclist increases speed by 1.25ft/s^2. a) If the motorcyclist starts from rest determine the time needed to reach an acceleration of 5.25ft/s^2. b)Determine the speed of the motorcyclist at the instant the acceleration is 7.00ft/s^2 c)Determine the magnitude of the acceleration at the instant the speed of the motorcyclist is 29ft/s.Determine the maximum constant speed of the motorcyclist when the maximum acceleration is 7.00ft/s^2.

Explanation / Answer

Radial acceleration =sqrt(5.25^2 -1.25^2) = 5.099 ft/sec^2 =v^2/r v = 45.162 ft/s t= v/a (tangential) = 40/1.25 = 36.129 s b) a(r) = sqrt(7^2-1.25^2) =v^2/r v^2 = a(r)*400 v= 52.488 ft/s c)29^2/400 = a(r) acceleration = sqrt ( a^2 +1.25^2) = 2.446 ft/s^2 d)52.488 ft/s

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