Final answer:
Without friction, a ball would continue to roll indefinitely at constant speed unless another force acts upon it. Friction, as a re-tarding force in the real world, is normally what slows down and stops a rolling ball.
Step-by-step explanation:
If there were no friction between a rolling ball and the ground, the ball would continue to roll indefinitely at a constant speed in the same direction, assuming no other forces act upon it (like air resistance). This is because, in the absence of friction, there would be no force to slow down or stop the ball. In the real world, friction is what eventually brings a rolling ball to a stop because it acts as a re-tarding force that converts kinetic energy into heat. Galileo's insights into motion suggested that an object in motion would remain in motion unless acted upon by an external force, such as friction.
For everyday experience, we can observe a similar effect on an air hockey table. When the air is turned on, the puck hovers slightly above the table, reducing friction and allowing it to glide smoothly. With friction drastically reduced, the puck can move much farther with very little change in speed. This represents what would happen to a rolling ball on a frictionless surface; it would continue its motion without slowing down.