Final answer:
The ball tethered to a stake travels in a circle with a constant speed, but its velocity's direction changes due to the force acting perpendicular to it, in the direction of the centripetal force.
Step-by-step explanation:
The ball attached to a tether and traveling in a circle at the full length of the tether experiences a force from the pull of the tether. This force acts in a direction perpendicular to the ball's velocity, and changes its direction. Specifically, the pull of the tether acts in the direction of the centripetal force, which is always directed towards the center of the circular path the ball is following. Consequently, while the ball maintains a constant speed due to the uniform circular motion, the direction of its velocity is constantly changing due to this centripetal force.
According to Newton's second law, an object will accelerate in the same direction as the net force applied to it, and since the centripetal force is directed towards the center of rotation, the object, or in this case, the ball, will also accelerate towards the center. This also means that a straight line from the circumference of the circle to the center is perpendicular to the tangential velocity of the object in motion.