We encourage you to interact with your colleagues here in conversations about this homework problem.
DISCUSSION and HINTS
With the polar description, we write the velocity and acceleration vectors for a point in terms of the polar unit vectors e_r and e_theta. Recall that e_r points outward from the observer O and the point P. The e_theta unit vector is perpendicular to e_r and points in the positive theta direction. These two unit vectors are shown in magenta in the above animated GIF. The velocity (in blue) is seen to be tangent to the path, as expected. The acceleration (in red) has both tangential and normal components: the normal component always points inward on the path, and the size and sign of the tangential component is directly tied to the rate of change of speed of P, also as expected.
In terms of problem solving, this problem is somewhat complicated in that the expression for r is in terms of the angle theta, instead of in terms of time. The time derivatives of r are found using the CHAIN RULE of differentiation. Please review the usage of the chain rule before solving this problem.