A book is at rest on a flat table. The book is pushed across the table causing it to move and eventually come to rest again how does the potential and kinetic energy change during this process
Initially, when the book is at rest on the flat table, its potential energy (relative to the table) remains constant, and its kinetic energy is zero (since it is not moving).
When the book is pushed across the table, it gains kinetic energy as its speed increases. The potential energy of the book remains fairly constant, assuming that the elevation of the book doesn't change significantly while moving across the table.
As the book continues to move across the table (assuming due to friction or another external force), it starts to slow down, which means that the kinetic energy is being converted to another form of energy, such as thermal energy due to the friction between the book and the table. The potential energy of the book still remains roughly constant.
Finally, when the book comes to rest again, its kinetic energy returns to zero, and the potential energy remains constant. Overall, during this process, the potential energy of the book has remained constant, and the kinetic energy has increased and decreased as the book gained and lost motion.