Final answer:
A ball rolling downhill on a curving ramp is in accelerated motion due to the constant force of gravity causing it to speed up and the centripetal acceleration stemming from the curvature of the ramp changing the ball’s direction.
Step-by-step explanation:
When a ball rolls downhill on a curving ramp, it is considered to be in accelerated motion for several reasons. Firstly, the gravity pulling the ball towards Earth causes it to accelerate downwards. This acceleration due to gravity is a constant downward force, which causes any object in freefall to increase its speed as it moves. The ball returns with the speed it had when it left, demonstrating a general property of free fall for any initial velocity.
Secondly, as the ball rolls down the curving ramp, there is a change in the direction of its velocity because of the ramp's curvature. This change in direction is also a form of acceleration, often referred to as centripetal acceleration. Centripetal acceleration occurs when an object moves in a circular path, which is the case when a ball follows a curving ramp. The force that keeps the ball moving along this curved path is the centripetal force, acting towards the center of the circular motion.
Therefore, the ball experiences both linear acceleration from gravity and centripetal acceleration from its curved trajectory. This dual aspect of the motion causes the velocity of the ball to change over time, either in speed, direction, or both, which, according to physics and specifically Newton's Second Law of Motion, defines accelerated motion.