To find which object has the greatest kinetic energy, we can use the kinetic energy formula:
\[ KE = \frac{1}{2}mv^2 \]
where \(KE\) is kinetic energy, \(m\) is mass, and \(v\) is velocity.
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Blue car (30 m/s): \[ KE = \frac{1}{2} \times 500 , \text{kg} \times (30 , \text{m/s})^2 = \frac{1}{2} \times 500 \times 900 = 225000 , \text{J} \]
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Red car (3 m/s): \[ KE = \frac{1}{2} \times 500 , \text{kg} \times (3 , \text{m/s})^2 = \frac{1}{2} \times 500 \times 9 = 2250 , \text{J} \]
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Yellow car (12 m/s): \[ KE = \frac{1}{2} \times 500 , \text{kg} \times (12 , \text{m/s})^2 = \frac{1}{2} \times 500 \times 144 = 36000 , \text{J} \]
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Green car (21 m/s): \[ KE = \frac{1}{2} \times 500 , \text{kg} \times (21 , \text{m/s})^2 = \frac{1}{2} \times 500 \times 441 = 110250 , \text{J} \]
Now we summarize the kinetic energy values:
- Blue car: 225,000 J
- Red car: 2,250 J
- Yellow car: 36,000 J
- Green car: 110,250 J
The object with the greatest kinetic energy is the blue car moving at 30 m/s with a kinetic energy of 225,000 J.