A wheel of radius 0.5 m rolls without sliding on a horizontal surface as shown. Starting from rest, the wheel moves with constant angular acceleration 6 rad/s². The distance in traveled by the center of the wheel from t = 0 to t = 3 s is: A) zero B) 27 m C) 13.5 m D) 18 m E) none of these

Question

Quizplus · Accepted Answer

First, we need to find the angular velocity of the wheel at t=3s.

ωf = ω0 + αt

ωf = 0 + 6(3)

ωf = 18 rad/s

Next, we can use the kinematic equations to find the displacement of the center of the wheel.

θ = ω0t + 1/2αt^2

θ = 0 + 1/2(6)(3)^2

θ = 27 rad

s = rθ

s = (0.5)(27)

s = 13.5 m

Therefore, the distance traveled by the center of the wheel from t=0 to t=3s is 13.5 m.

The correct answer is C) 13.5 m.

A Wheel of Radius 0