Kinetic Energy Proportional to Speed Squared

Steps:

• Kinetic energy formula: KE = (1/2) m v².
• Initial KE: 1500 J = (1/2) m (10)², so (1/2) m = 1500 / 100 = 15 kg m²/s².
• New speed: 40 m/s, so new KE = 15 × (40)² = 15 × 1600 = 24000 J.
• Speed increases 4-fold, KE increases by 4² = 16 times: 1500 × 16 = 24000 J.

Why C is correct:

• KE = (1/2)mv² shows energy scales with v²; 4× speed yields 16× KE.

Why the others are wrong:

• A: Assumes linear speed increase (3×), ignores v².
• B: Assumes linear with speed change (4×), ignores v².
• D: Assumes linear with new speed (10×), ignores v².

Final answer: C