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Which has greater kinetic energy, a car traveling at 30 km/h or a half-as-massive car traveling at 60 km/h?

A) Car at 30 km/h
B) Car at 60 km/h
C) Both have the same kinetic energy
D) Cannot be determined

User Zbdiablo
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1 Answer

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Final answer:

The car traveling at 60 km/h has greater kinetic energy because kinetic energy is directly proportional to the square of the velocity, and the second car, although half-as-massive, is traveling at a speed that is squared in the energy calculation.

Step-by-step explanation:

To determine which car has greater kinetic energy, we can use the formula for kinetic energy, KE = ½mv², where m is mass and v is velocity. Let's assume that the mass of the first car is M and the second car has a mass of ½M, since it is half-as-massive. If the first car is traveling at 30 km/h and the second at 60 km/h, to compare their kinetic energies, we convert their velocities to the same units (m/s) and plug into the formula:

First car: KE1 = ½ × M × (30 km/h × 1000 m/km / 3600 s/h)²

Second car: KE2 = ½ × (½M) × (60 km/h × 1000 m/km / 3600 s/h)²

It is evident after simplifying the equations that the kinetic energy of the second car will be greater, since velocity has a squared relationship with kinetic energy. Therefore, the correct answer is B) Car at 60 km/h.

User Benjamin Smith Max
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