A ball is lodged in a hole in the floor near the outside edge of a merry-go-round that is turning at constant speed. Which kinematic variable or variables change with time, assuming that the position is measured from an origin at the center of the merry-go-round?

a.the position of the ball only
b.the velocity of the ball only
c.the acceleration of the ball only
d.both the position and velocity of the ball
e.the position and velocity and acceleration of the ball

do the magnitudes of the position, velocity, and acceleration vectors change with time?

yes or no?

The kinematic variables that change with time in this scenario are the position and velocity of the ball. The correct answer to the first question is option (d), both the position and velocity of the ball change with time.

To understand why, let's break it down:

1. The position of the ball changes because it is moving along the merry-go-round as it rotates. Since the ball is lodged in a hole at the outside edge of the merry-go-round, its distance from the origin (center of the merry-go-round) changes as it moves around.

2. The velocity of the ball also changes because it is constantly moving in a circular path. A velocity vector has both magnitude and direction. In this case, the magnitude of the ball's velocity remains constant because the merry-go-round is turning at a constant speed. However, the direction of the velocity vector changes as the ball moves around the merry-go-round.

Now, moving on to the second question:

Do the magnitudes of the position, velocity, and acceleration vectors change with time? Yes, the magnitudes of the position, velocity, and acceleration vectors all change with time in this scenario.

Let's break it down:

1. The magnitude of the position vector changes because the ball is moving in a circular path, and the distance from the origin (center of the merry-go-round) changes as it moves.

2. The magnitude of the velocity vector remains constant because the merry-go-round is turning at a constant speed. However, the direction of the velocity vector changes, as explained earlier.

3. The magnitude of the acceleration vector also changes because acceleration is related to changes in velocity. As the direction of the ball's velocity vector changes, it experiences a centripetal acceleration towards the center of the merry-go-round.

Therefore, the answer to the second question is yes, the magnitudes of the position, velocity, and acceleration vectors all change with time.

duplicate post; already answered