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/no?

e

no

The magnitudes of all of those quantities remain the same, but the directions change as it rotates.

In this scenario, the position of the ball, the velocity of the ball, and the acceleration of the ball all change with time.

The correct option to choose from the given choices is d. both the position and velocity of the ball.

When the ball is lodged in the hole on the merry-go-round, its position changes as the merry-go-round rotates, thereby changing the position of the ball relative to the origin.

Additionally, the ball moves in a circular path due to the constant speed of the merry-go-round, resulting in a changing velocity vector. The magnitude of the velocity remains constant, but the direction of the velocity vector changes as the ball rotates.

Furthermore, since the direction of the velocity vector is changing, the ball experiences an acceleration towards the center of the merry-go-round, known as centripetal acceleration. Therefore, the acceleration of the ball also changes with time.

To summarize: the position, velocity, and acceleration of the ball all change with time when a ball is lodged on a merry-go-round.

Yes, the magnitudes of the position, velocity, and acceleration vectors change with time.

To determine which kinematic variables change with time when a ball is lodged in a hole near the outside edge of a merry-go-round, we need to consider the motion of the ball in relation to the rotating merry-go-round.

First, let's address the given options:

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, velocity, and acceleration of the ball

Based on the scenario described, the position of the ball will change as the merry-go-round rotates. This means that option a is correct, and the position of the ball changes with time.

When the position of an object changes with time, its velocity also changes. In this case, the ball will experience a change in velocity due to its rotational motion on the merry-go-round. This means that option b is also correct, and the velocity of the ball changes with time.

Acceleration, on the other hand, is the rate of change of velocity. While the ball is rotating on the merry-go-round, it experiences a centripetal acceleration towards the center of the rotation. This acceleration is constant in magnitude but does not change with time unless the rotational speed of the merry-go-round changes. Thus, option c is incorrect, and the acceleration of the ball does not change with time.

Therefore, the correct answer to the first part of the question is option d - both the position and velocity of the ball change with time.

Regarding the magnitude of the position, velocity, and acceleration vectors, the answer is "yes." Since the ball is undergoing non-uniform circular motion, the magnitudes of the position, velocity, and acceleration vectors change with time. The position vector describes the position of the ball with respect to the origin at the center of the merry-go-round. The velocity vector describes the rate of change of the position vector, i.e., the speed and direction of the ball's motion. The acceleration vector represents the change in the velocity vector, directing the ball towards the center of rotation. Therefore, the magnitudes of all these vectors vary as the ball moves on the rotating merry-go-round.

In summary:
- The position of the ball changes with time.
- The velocity of the ball changes with time.
- The acceleration of the ball does not change with time (unless the rotational speed of the merry-go-round changes).
- The magnitudes of the position, velocity, and acceleration vectors change with time.