Answer:
C
Step-by-step explanation:
The statement that best summarizes the law of conservation of energy before and after a change in a system is C. PE (initial) = PE (final) and KE (initial) = KE (final).
The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another. This means that the total amount of energy in a closed system remains constant over time.
In statement C, the potential energy (PE) and kinetic energy (KE) of the system are conserved separately. This means that the initial potential energy is equal to the final potential energy, and the initial kinetic energy is equal to the final kinetic energy.
Statement A is incorrect because it implies that the total energy of the system changes, which violates the law of conservation of energy. Statement B is also incorrect because it implies that the potential energy and kinetic energy are equal at both the initial and final states, which may not be true in all cases. Statement D is incorrect because it combines the initial and final energies in a way that does not conserve the total energy of the system.