Asked by aw2
Calculate the momentum of cars A and B, and then answer the question.
Car A:
Mass: 1,000 kilograms
Velocity: 40 meters/second
Car B:
Mass: 4,000 kilograms
Velocity: 10 meters/second
Which car is harder to stop and why?
All Answers 1
Answered by
GPT-5 mini
AI
Momentum p = m v.
- Car A: pA = 1,000 kg × 40 m/s = 40,000 kg·m/s.
- Car B: pB = 4,000 kg × 10 m/s = 40,000 kg·m/s.
So both cars have the same momentum; they require the same impulse (change in momentum) to stop, so in that sense they are equally “hard to stop.”
Note: their kinetic energies differ:
- KE_A = 0.5·1,000·40^2 = 800,000 J
- KE_B = 0.5·4,000·10^2 = 200,000 J
Because Car A has four times the kinetic energy, it requires more energy to be dissipated by the brakes. Depending on the stopping mechanism and limits (maximum braking force, available friction, brake heat capacity), this can make Car A take longer distance or stress brakes more — even though the required impulse is the same.
- Car A: pA = 1,000 kg × 40 m/s = 40,000 kg·m/s.
- Car B: pB = 4,000 kg × 10 m/s = 40,000 kg·m/s.
So both cars have the same momentum; they require the same impulse (change in momentum) to stop, so in that sense they are equally “hard to stop.”
Note: their kinetic energies differ:
- KE_A = 0.5·1,000·40^2 = 800,000 J
- KE_B = 0.5·4,000·10^2 = 200,000 J
Because Car A has four times the kinetic energy, it requires more energy to be dissipated by the brakes. Depending on the stopping mechanism and limits (maximum braking force, available friction, brake heat capacity), this can make Car A take longer distance or stress brakes more — even though the required impulse is the same.
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