The kinetic energy (KE) of an object can be calculated using the formula:
\[ KE = \frac{1}{2} mv^2 \]
where \( m \) is the mass and \( v \) is the velocity of the object.
Let’s calculate the kinetic energy for each car:
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Green car (500 kg, 21 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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Yellow car (500 kg, 12 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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Red car (500 kg, 3 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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Blue car (500 kg, 30 m/s): \[ KE = \frac{1}{2} \times 500 \times (30)^2 = \frac{1}{2} \times 500 \times 900 = 225000 , \text{J} \]
Now, let's summarize the kinetic energy for each car:
- Green car: 110250 J
- Yellow car: 36000 J
- Red car: 2250 J
- Blue car: 225000 J
The object with the greatest kinetic energy is the blue car with a mass of 500 kg moving at 30 m/s, which has a kinetic energy of 225000 J.