Kinetic energy proportional to speed squared

Steps:

• Kinetic energy formula: KE = (1/2)mv², where m is mass and v is speed.
• If KE increases by factor of 4, new KE = 4 × original KE.
• Mass m remains constant, so (v_new)² / (v_old)² = 4.
• Thus, v_new / v_old = √4 = 2.

Why A is correct:

• KE ∝ v², so doubling speed quadruples KE per the formula.

Why the others are wrong:

• B: Assumes direct proportionality between KE and v, ignoring the square.
• C: Might confuse with momentum or tripled effects, not applicable here.
• D: Equals (factor for KE)², reversing the relationship.

Final answer: A