Discussion and hints:

For the polar description to be used here, the radial unit vector e_R points from O toward B. The transverse unit vector e_θ is perpendicular to e_R and points in the direction of increasing angle θ (counterclockwise from e_R).

The first time derivative of θ  is given to the the constant ω. Therefore, the second time derivative of θ  is zero. The time derivatives of R are found from direct differentiation of the path equation R = bθ . These results then are used to find the v_P and a_P in terms of their polar coordinates.

Carefully watch the animation below of the motion of P. As we have seen before, the velocity vector is always tangent to the path, whereas the acceleration vector has both tangent and normal components. The normal component always points inward to the path. Also, as we have seen before, when the angle between v_P and a_P is less than 90°, the speed of P is increasing. As you can see from the animation below, the speed of P is increasing throughout the entire motion.

Any questions??