When an object is moving with uniform circular motion, the object's tangential speed
a. is circular
b. is perpendicular to the plane of motion
c. is constant
d. is directed toward the center of motion
and why is it correct?

c. is constant

Explanation:

The rotational motion with the uniform angular velocity has a constant tangential speed.But its velocity component is variable and changes its direction at every point.The direction of the velocity is along the tangential line in the plane of motion and perpendicular to the radius of circular.But the magnitude of the velocity called speed is constant throughout the motion if it has a constant angular velocity. The linear velocity is related to the angular velocity by the formula                                            

                                              v = rω

Alinear relationship would look like a straight line on the graph. it could have a positive negative or 0 slope. so it could be a line potentially going in any direction but it must be perfectly straight.