Elastic collisions conserve both momentum and kinetic energy

Steps:

• Define elastic collision: one where total kinetic energy and linear momentum are both conserved.
• Evaluate option A: relative speed of approach equals separation, which follows from momentum and energy conservation.
• Evaluate option B: total kinetic energy conserved, a core property of elastic collisions.
• Evaluate option C: kinetic energy reduced, which describes inelastic collisions instead.
• Evaluate option D: total linear momentum conserved, true for all collisions in isolated systems.

Why C is correct:

• In elastic collisions, the total kinetic energy remains unchanged, as per the law of conservation of kinetic energy (KE_final = KE_initial).

Why the others are wrong:

• A: This equality holds in elastic collisions due to symmetric velocity reversal in the center-of-mass frame.
• B: Kinetic energy conservation is the defining feature distinguishing elastic from inelastic collisions.
• D: Momentum conservation applies to all collisions, including elastic ones, per Newton's third law.

Final answer: C