To determine which object has the greatest kinetic energy, we can use the formula for kinetic energy:
\[ KE = \frac{1}{2} mv^2 \]
where \( m \) is the mass of the object and \( v \) is its velocity.
All the cars have the same mass of 500 kg, so we only need to consider their speeds:
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Yellow car at 12 m/s: \[ KE = \frac{1}{2} \times 500 , \text{kg} \times (12 , \text{m/s})^2 = 0.5 \times 500 \times 144 = 36000 , \text{J} \]
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Green car at 21 m/s: \[ KE = \frac{1}{2} \times 500 , \text{kg} \times (21 , \text{m/s})^2 = 0.5 \times 500 \times 441 = 110250 , \text{J} \]
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Blue car at 30 m/s: \[ KE = \frac{1}{2} \times 500 , \text{kg} \times (30 , \text{m/s})^2 = 0.5 \times 500 \times 900 = 225000 , \text{J} \]
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Red car at 3 m/s: \[ KE = \frac{1}{2} \times 500 , \text{kg} \times (3 , \text{m/s})^2 = 0.5 \times 500 \times 9 = 2250 , \text{J} \]
Now, comparing the kinetic energies calculated:
- Yellow car: 36,000 J
- Green car: 110,250 J
- Blue car: 225,000 J
- Red car: 2,250 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.