Question

a book is falling from the top shelf of a bookcase. which statement correctly describes the change in the energy of the book?
the kinetic energy remains at zero, but potential energy increases.
the potential energy and kinetic energy remain the same.
the potential energy decreases as kinetic energy increases.
the kinetic energy decreases as potential energy increases.

Explanation:

When a book falls, its height decreases, so gravitational potential energy (dependent on height: $PE=mgh$) decreases. At the same time, its speed increases, so kinetic energy (dependent on speed: $KE=\frac{1}{2}mv^2$) increases. Energy is converted between these forms (ignoring air resistance, total mechanical energy is conserved).

Answer:

The potential energy decreases as kinetic energy increases.