To solve the problem, we need to determine the velocities of points O and A on a rigid circular disc rolling without slipping on a flat surface.

Given:

• The radius of the disc is r (in meters).
• The angular velocity of the disc is \omega (in rad/s).

Concept: For a disc rolling without slipping on a flat surface, the point of contact (point A) with the ground has zero velocity, as it momentarily comes to rest before rolling over.

Velocities at Points O and A:

1. Velocity at Point O:

   The center of the disc (point O) moves with a velocity due to the rotation of the disc. The linear velocity v_O of point O is given by:

   v_O = r\omega

   The direction of this velocity is along the horizontal axis (positive \hat{i} direction), hence:

   v_O = r\omega \hat{i}

2. Velocity at Point A:

   Point A is the point of contact with the ground during rolling without slipping. At any instant, the velocity of this point is zero because it is instantaneously at rest:

   v_A = 0

Therefore, the velocities at points O and A are r\omega\hat{i} and 0, respectively.

Conclusion: The correct answer is r\omega\hat{i} and 0.