91Ó°ÊÓ

Kinetic energy is the energy that an object possesses due to its motion. It can be calculated using the formula \( KE = \frac{1}{2} m v^2 \), where \( m \) is the mass of the object and \( v \) is its velocity. For the book in our exercise, we first determine its kinetic energy at point A using its mass of 1.50 kg and velocity of 3.21 m/s. This calculation helps us understand how much energy the book has at the start of the journey along the rough surface. Similarly, the kinetic energy at point B is calculated with the updated velocity of 1.25 m/s. By comparing these two kinetic energy values, we can track how the motion and energy of the book change over time. This is the foundation for understanding the work done on the book as it moves.

Work done on an object is a measure of energy transfer that occurs when a force acts on the object to move it over a distance. When considering how much work was done on the book between points A and B, it's crucial to understand that it's determined by the change in kinetic energy. The formula utilized is \( W_{AB} = KE_B - KE_A \), highlighting that work done is essentially the difference in the book's kinetic energy between these two points. In our scenario, the calculated work reveals the amount of energy lost to friction on the rough surface, which causes the book to slow down as it approaches point B.

A change in velocity occurs when an object speeds up or slows down as a result of forces acting on it. In our exercise, between points A and B, the book experiences a reduction in velocity due to the negative work done by friction. Afterwards, the problem explores how additional work done affects velocity at point C. Negative work, meaning work done against the motion, further reduces the kinetic energy and thus the velocity. Conversely, positive work adds energy, allowing the book to speed up. By understanding these scenarios, we appreciate how work, whether positive or negative, directly influences an object's speed and direction.

The conservation of energy principle states that energy cannot be created or destroyed, only transformed from one form to another. In our problem, we see the transition of energy from kinetic energy to work against external forces like friction. As the book transitions from point A to C through B, the work-energy theorem is applied to reflect these energy changes. In practical terms, the energy initially present in the book's motion is partially transformed into work done against friction, causing a velocity change. The book's final speed at point C depends on this energy transformation, showcasing the broader theme of energy conservation in automotive motion.