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Kinetic energy depends on speed squared rather than on speed alone. What does this imply when comparing a car traveling at 100 km/h with the same car traveling at 50 km/h?
AThe faster car has twice the kinetic energy of the slower one
BThe faster car has four times the kinetic energy of the slower one
CBoth cars have exactly the same kinetic energy
DThe faster car has half the kinetic energy of the slower one
Answer & Solution
Correct answer: B. The faster car has four times the kinetic energy of the slower one
1. Kinetic energy is proportional to the square of speed, KE = one half m v squared.
2. Doubling the speed from 50 km/h to 100 km/h means v squared increases by a factor of four, since 2 squared is 4.
3. Because mass stays the same, the kinetic energy at 100 km/h is therefore four times the kinetic energy at 50 km/h, not twice or the same.
4. This proportionality to speed squared, rather than to speed itself, is part of why high-speed collisions are so much more destructive than low-speed ones.
_Source: OpenStax College Physics (CC BY 4.0), Ch 7 "Work, Energy, and Energy Resources", section 7.2 Kinetic Energy and the Work-Energy Theorem_
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