The correct understanding of how potential and kinetic energy change during the process described would be as follows:
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Potential Energy (PE): The potential energy of the book remains constant while it is on the table, as long as its height relative to a reference point does not change. In this case, since the book stays on the table throughout the process, the potential energy stays the same.
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Kinetic Energy (KE): When the person shoves the book, its kinetic energy increases as it gains speed. As the book slides across the table, it gradually loses kinetic energy due to friction until it eventually comes to rest. Therefore, the kinetic energy decreases until it reaches zero when the book stops moving.
Taking this into account, the most accurate response 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."