To determine which object has the greatest kinetic energy, we can use the formula for kinetic energy (KE):
\[ KE = \frac{1}{2}mv^2 \]
where \(m\) is the mass of the object and \(v\) is its velocity.
Given that all cars have the same mass of 500 kg, we can compare their kinetic energies by calculating \(v^2\) for each one.
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Red car: \(v = 3 , \text{m/s}\) \[ KE = \frac{1}{2} \times 500 \times (3)^2 = \frac{1}{2} \times 500 \times 9 = 2250 , \text{J} \]
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Yellow car: \(v = 12 , \text{m/s}\) \[ KE = \frac{1}{2} \times 500 \times (12)^2 = \frac{1}{2} \times 500 \times 144 = 36000 , \text{J} \]
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Green car: \(v = 21 , \text{m/s}\) \[ KE = \frac{1}{2} \times 500 \times (21)^2 = \frac{1}{2} \times 500 \times 441 = 110250 , \text{J} \]
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Blue car: \(v = 30 , \text{m/s}\) \[ KE = \frac{1}{2} \times 500 \times (30)^2 = \frac{1}{2} \times 500 \times 900 = 225000 , \text{J} \]
Now, we can compare the kinetic energies calculated:
- Red car: 2250 J
- Yellow car: 36000 J
- Green car: 110250 J
- Blue car: 225000 J
The blue car moving at 30 m/s has the greatest kinetic energy of 225,000 J.
Answer: A blue car with a mass of 500 kg moving at 30 m/s.
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