A motorcyclist travels around a curved path that has a radius of 225 . While tra

Question

A motorcyclist travels around a curved path that has a radius of 225 . While traveling around the curved path, the motorcyclist increases speed by 1.1ft/s^2 .

a) If the motorcyclist starts from rest, determine the time needed to reach an acceleration of 4.5ft/s .

b) Determine the speed of the motorcyclist at the instant the acceleration is 6.5ft/s^2 .

c) Determine the magnitude of the acceleration at the instant the speed of the motorcyclist is 26ft/s .

d) Determine the maximum constant speed of the motorcyclist when the maximum acceleration is 6.5ft/s^2 .

Explanation / Answer

tangential acceleration = 1.1 ft / sec2

centripetal acceleration = v^2 / r

at time t .... v = 1.1 * t

so magnitude of net acceleltiaon = ( 1.1^2 + centripetal acc^2 ) = 4.5^2

so.. centripetal acc = 4.3635 ft/sec2

so.. v^2 / r = 4.3635

v^2 / 225 = 4.3634

so v = 31.333 ft/sec

so.... 1.1 * t = 31.33343

a)

so time t = 28.48494 secs

b)  

magnitude of net acceleltiaon = ( 1.1^2 + centripetal acc^2 ) = 6.5^2

so.. centripetal acc = 6.40625 ft/sec2

so.. v^2 / r = 6.40625

v^2 / 225 = 6.40625

so v = 37.966 ft/sec

c) v = 26 ft / sec

so centripetal acceleration = v^2 / r = 26^2 / 225 = 3.00444 ft /s ec2

so total acceleration = sqrt ( 1.1^2 + 3.00444^2 ) = 3.19948 ft / sec2

d) for constant speed...

v^2 / r = 6.5

v^2 / 225 = 6.5

so v = 38.2426 ft/sec

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