Learning Goal To analyze the motion of a body that is traveling along a curved p

Question

Learning Goal To analyze the motion of a body that is traveling along a curved path, to determine the body's acceleration, velocity, and position. A motorcyclist travels around a curved path that has a radius of 375 ft. While traveling around the curved path, the motorcyclist increases speed by 1.10 ft/s Part A-Finding the time interval for the motorcyclist to reach a given acceleration If the motorcyclist starts from rest, determine the time needed to reach an acceleration of 5.75 ft/s2 Express your answer to three significant figures and include the appropriate units. View Available Hint(s) 0? t-1 Value Units Submit Part B -Speed of the Motorcyclist at a Given Acceleration Determine the speed of the motorcyclist at the instant the acceleration is 7.25 ft/s2 Express your answer to three significant figures and include the appropriate units. View Available Hint(s) u=1 Value Units Submit Part C-Magnitude of the Motorcyclist's Acceleration at a Given Speed Determine the magnitude of the acceleration at the instant the speed of the motorcyclist is 20.5 ft/s. Express your answer to three significant figures and include the appropriate units. View Available Hint(s) a=1 Value l Units Submit

Explanation / Answer

Part A )

aR = ( 5.752 - 1.12 )1/2   

aR = 5.64 ft/s2

v = ( aR X r )1/2

v = ( 5.64 X 375 )1/2

v = 45.99 ft/s

t = v / at

t = 45.99 / 1.1

t = 41.809 sec

Part B )

aR = ( 7.252 - 1.12 )1/2   

aR = 7.166 ft/s2

v = ( aR X r )1/2

v = ( 7.166 X 375 )1/2

v = 51.838 ft/s

Part C )

aR = v2 / r

= 20.52 / 375

= 1.12 ft/s2

a = ( aR2 + at2 )1/2

a = ( 1.122 + 1.12 )1/2

a = 1.569 ft/s2

Part D )

aR = ( a2 - at2 )1/2   

= ( 7.252 - 1.12 )1/2

= 7.166 ft/s2

vmax2 / r = aR

vmax = ( aR X r )1/2

= ( 7.166 X 375 )1/2

vmax = 51.838 ft/s

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