Sure, let's solve this step-by-step.
1. Identify the mass and velocity of the car:
- Mass [tex]\( m = 600 \, \text{kg} \)[/tex]
- Velocity [tex]\( v = 12 \, \text{m/s} \)[/tex]
2. Write down the formula for kinetic energy:
[tex]\[
KE = \frac{1}{2} m v^2
\][/tex]
3. Substitute the known values into the formula:
[tex]\[
KE = \frac{1}{2} \times 600 \, \text{kg} \times (12 \, \text{m/s})^2
\][/tex]
4. First find [tex]\( v^2 \)[/tex], the square of the velocity:
[tex]\[
v^2 = (12 \, \text{m/s})^2 = 144 \, \text{m}^2/\text{s}^2
\][/tex]
5. Now, multiply by the mass [tex]\( m \)[/tex]:
[tex]\[
600 \, \text{kg} \times 144 \, \text{m}^2/\text{s}^2 = 86400 \, \text{kg} \cdot \text{m}^2/\text{s}^2
\][/tex]
6. Finally, multiply by [tex]\( \frac{1}{2} \)[/tex]:
[tex]\[
KE = \frac{1}{2} \times 86400 \, \text{kg} \cdot \text{m}^2/\text{s}^2 = 43200 \, \text{J}
\][/tex]
Thus, the kinetic energy of the car is [tex]\( \mathbf{43,200 \, \text{J}} \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{43,200 \, \text{J}} \][/tex]
