Kinetic energy relates to momentum via KE = p²/2m

Steps:

• Recall kinetic energy formula: KE = p² / (2m), where p is momentum and m is mass.
• Initial kinetic energy: KE_initial = p² / (2m).
• Final kinetic energy: KE_final = p₀² / (2m).
• Increase in kinetic energy: ΔKE = KE_final - KE_initial = (p₀² - p²) / (2m).

Why A is correct:

• Matches the difference of kinetic energies using the formula KE = p² / (2m).

Why the others are wrong:

• B: Incorrectly squares the momentum difference instead of taking the difference of squares.
• C: Omits squares on momenta and misplaces the division by 2m.
• D: Lacks parentheses, yielding p₀² - (p² / 2m), which alters the expression.

Final answer: A