Kinetic energy depends on mass and the square of speed

Steps:

• Kinetic energy formula: KE = ½ m v².
• For car P: KE_P = ½ m v² = 240 J.
• For car Q: mass_Q = ½ m_P, speed_Q = 2 v_P.
• KE_Q = ½ (½ m) (2 v)² = ½ (½ m) (4 v²) = (½)(2 m v²) = 2 × (½ m v²) = 2 × 240 J = 480 J.

Why C is correct:

• KE scales linearly with mass and quadratically with speed, so factor = (½) × (2)² = 2, yielding 2 × 240 J = 480 J per the KE formula.

Why the others are wrong:

• A: Assumes only half mass halves KE, ignoring speed increase.
• B: Assumes no net change, ignoring mass and speed effects.
• D: Overmultiplies by assuming speed factor of 4 without halving mass.

Final answer: C