To determine which object has the greatest kinetic energy, we can use the kinetic energy formula:
\[ KE = \frac{1}{2}mv^2 \]
where:
- \( KE \) is the kinetic energy
- \( m \) is the mass of the object
- \( v \) is the velocity of the object
Since all the cars have the same mass (500 kg), we only need to compare their velocities to find the one with the highest kinetic energy.
Let's calculate the kinetic energy for each car:
-
Yellow car: \[ KE = \frac{1}{2} \times 500 , \text{kg} \times (12 , \text{m/s})^2 = 0.5 \times 500 \times 144 = 36000 , \text{J} \]
-
Blue car: \[ KE = \frac{1}{2} \times 500 , \text{kg} \times (30 , \text{m/s})^2 = 0.5 \times 500 \times 900 = 225000 , \text{J} \]
-
Red car: \[ KE = \frac{1}{2} \times 500 , \text{kg} \times (3 , \text{m/s})^2 = 0.5 \times 500 \times 9 = 2250 , \text{J} \]
-
Green car: \[ KE = \frac{1}{2} \times 500 , \text{kg} \times (21 , \text{m/s})^2 = 0.5 \times 500 \times 441 = 110250 , \text{J} \]
Now let's compare all the calculated kinetic energies:
- Yellow car: 36,000 J
- Blue car: 225,000 J
- Red car: 2,250 J
- Green car: 110,250 J
The blue car with a mass of 500 kg moving at 30 m/s has the greatest kinetic energy, which is 225,000 Joules.