Question #11400124

# What would be the linear displacement of the tire's axle as it moves forward from t=0sec to t=15 sec?

**Starting from rest at t=0sec, a tire on a mountain bike has a constant angular acceleration. When t= 5 sec, the angular velocity of the wheel is 6.5 rad/sec. The angular acceleration continues until t= 15 sec, after which the angular velocity remains constant. The tire has a radius of 22 cm.
Angular velocity (final) and acceleration were found through out this problem:
Ï‰f = 19.5 rad/s
Î± = 1.3 rad/s^2
Along with total angular displacement:
Î˜ = 146.25 rad
And total displacement:
Î”s = 32.175 m
**

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linear displacement tire 039 s forward t 0sec Starting t 0sec mountain constant angular acceleration angular velocity rad sec angular acceleration continues angular velocity remains constant radius cm
Angular velocity final acceleration through problem
Ï‰f rad s
Î± rad s 2
Along angular displacement
Î˜ 146 25 rad
And displacement
Î”s 32 175