The correct response to how the potential and kinetic energy change during the process is:
"The potential energy will stay the same as long as the book stays on the table. The kinetic energy increases when the book is shoved and then gradually decreases as it slides across the table and then comes to rest on the edge."
Here's why this response is accurate:
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Potential Energy: Since the book remains on the flat table throughout the entire process, its gravitational potential energy remains constant. This is because potential energy in this context is determined by the height of the object above a reference point (the table surface), and that height does not change.
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Kinetic Energy: When the person gives the book a shove, its velocity increases, which means the kinetic energy of the book increases at that moment. As it slides across the table, it experiences friction (assuming the table is not perfectly smooth), which opposes the motion. This causes the kinetic energy to decrease until the book comes to rest.
Therefore, the potential energy stays the same while the kinetic energy increases when shoved and decreases as the book slides to a stop.