To determine the kinetic energy of the car, we use the kinetic energy formula:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
where:
- [tex]\( KE \)[/tex] is the kinetic energy,
- [tex]\( m \)[/tex] is the mass of the car,
- [tex]\( v \)[/tex] is the velocity of the car.
Given:
- [tex]\( m = 600 \, \text{kg} \)[/tex]
- [tex]\( v = 12 \, \text{m/s} \)[/tex]
We substitute these values into the formula:
[tex]\[ KE = \frac{1}{2} \times 600 \, \text{kg} \times (12 \, \text{m/s})^2 \][/tex]
First, compute the square of the velocity:
[tex]\[ (12 \, \text{m/s})^2 = 144 \, \text{(m/s)}^2 \][/tex]
Next, multiply the mass by the squared velocity:
[tex]\[ 600 \, \text{kg} \times 144 \, \text{(m/s)}^2 = 86,400 \, \text{kg} \cdot \text{m}^2 \cdot \text{s}^{-2} = 86,400 \, \text{J} \][/tex]
Now, multiply by [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[ KE = \frac{1}{2} \times 86,400 \, \text{J} = 43,200 \, \text{J} \][/tex]
Therefore, the kinetic energy of the car is [tex]\( 43,200 \, \text{J} \)[/tex].
Thus, the correct answer is:
[tex]\[ 43,200 \, \text{J} \][/tex]
