The correct response to how the potential and kinetic energy change during the process described 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 the reasoning:
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Potential Energy: While the book remains on the table, its height relative to the ground doesn’t change significantly, so the gravitational potential energy remains constant.
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Kinetic Energy: Initially, when the book is at rest, its kinetic energy is zero. When the person shoves the book, its kinetic energy increases as it gains speed. As it slides across the table, friction acts on the book, causing it to lose speed and, consequently, kinetic energy until it eventually comes to rest again.