Which has more kinetic energy: a 1000 kg car traveling at 10 m/s, or a 500 kg motorcycle traveling at 20 m/s?

Kinetic energy KE = ½mv². Calculate both:

Car: ½ × 1000 × 10² = 500 × 100 = 50,000 J.

Motorcycle: ½ × 500 × 20² = 250 × 400 = 100,000 J. Motorcycle has twice the KE despite half the mass — because velocity is SQUARED in the formula. Implications: (1) DOUBLING SPEED quadruples KE (and stopping distance for same deceleration); (2) Same KE can come from very different mass-speed combinations; (3) Energy-of-motion explanations: faster moving objects do more damage in collisions; cars hitting things at highway speeds release dramatically more energy than at city speeds; (4) Engineering: vehicles need brakes proportional to KE not mass; aircraft must shed huge KE during landing (a 200,000 kg aircraft at 80 m/s has KE = ½ × 200,000 × 6400 = 640,000,000 J or 640 MJ — equivalent to several gallons of gasoline burning). Kinetic energy types: TRANSLATIONAL (linear motion, ½mv²), ROTATIONAL (½Iω², where I is moment of inertia and ω is angular velocity), VIBRATIONAL (in atomic-scale motion = thermal energy). Energy units: Joule (SI) = kg·m²/s²; calorie (food); BTU (heat); kWh (electricity); foot-pound; erg. Energy conversion: 1 cal ≈ 4.18 J; 1 BTU ≈ 1055 J; 1 kWh = 3.6 × 10⁶ J. Energy in collisions: at impact, KE converts to deformation, heat, sound, and other forms; safety design (crumple zones, airbags) extends collision time to spread KE conversion over more time = less peak force. ASVAB MC tests this conceptually — usually doesn't require complex calculation but does test that velocity affects KE more strongly than mass.