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 speed.
Given that all the cars have the same mass (500 kg), we can simplify the comparison by focusing on the speed squared (\( v^2 \)).
Let's calculate the kinetic energy for each car:
-
Green Car:
Mass = 500 kg, Speed = 21 m/s
\[ KE = \frac{1}{2} \times 500 \times (21)^2 = \frac{1}{2} \times 500 \times 441 = 110250 \text{ J} \] -
Yellow Car:
Mass = 500 kg, Speed = 12 m/s
\[ KE = \frac{1}{2} \times 500 \times (12)^2 = \frac{1}{2} \times 500 \times 144 = 36000 \text{ J} \] -
Red Car:
Mass = 500 kg, Speed = 3 m/s
\[ KE = \frac{1}{2} \times 500 \times (3)^2 = \frac{1}{2} \times 500 \times 9 = 2250 \text{ J} \] -
Blue Car:
Mass = 500 kg, Speed = 30 m/s
\[ KE = \frac{1}{2} \times 500 \times (30)^2 = \frac{1}{2} \times 500 \times 900 = 225000 \text{ J} \]
Now, comparing the kinetic energies:
- Green Car: 110250 J
- Yellow Car: 36000 J
- Red Car: 2250 J
- Blue Car: 225000 J
The blue car, having a speed of 30 m/s, has the greatest kinetic energy of 225000 J.