a. For the same speed, the acceleration of the object varies _____________ (directly, inversely) with the radius of curvature.

The acceleration of an object for the same speed varies inversely with the radius of curvature. This is because acceleration is the rate of change of velocity per unit of time. When an object is moving in a circular path, the direction of its velocity is constantly changing, even if its speed remains the same. This change in direction is a type of acceleration known as centripetal acceleration. The formula for centripetal acceleration is a = v^2/r, where v is the speed of the object and r is the radius of curvature. Therefore, for a given speed, the acceleration of the object is inversely proportional to the radius of curvature. If the radius of curvature increases, the acceleration decreases, and vice versa.