Kinetic energy from momentum formula

Steps:

• Momentum p = mv, so v = p/m; kinetic energy KE = p²/(2m).
• Initial KE = p²/(2m).
• Final momentum = 2p, so final KE = (2p)²/(2m) = 4p²/(2m).
• Increase in KE = final KE - initial KE = [4p²/(2m)] - [p²/(2m)] = 3p²/(2m).

Why A is correct:

• A represents the difference in squared momenta over 2m, matching ΔKE = [(2p)² - p²]/(2m) = 3p²/(2m) per the KE formula.

Why the others are wrong:

• B gives final KE only, ignoring subtraction of initial KE.
• C gives initial KE, not the increase.
• D duplicates B, yielding final KE instead of change.

Final answer: A