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Physics angular acceleration problem assistance?

A ball of radius 0.50 m rolls without slipping on a horizontal surface as shown below. Starting from rest at t = 0, the ball moves with constant angular acceleration 6.0 rad/s2. What is the distance, in meters, traveled by the center of the ball from t = 0 to t = 3.0 s?

The pic is simply a ball moving from left to right on a horizontal plane. All information is provided above.

I'd appreciate any explanation, as opposed to just algebra =)

Thank you!

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