Let’s determine the kinetic energy of the race car using the known formula for kinetic energy.
1. Identify the given values:
- Mass ([tex]\( m \)[/tex]) of the race car: [tex]\( 700 \, \text{kg} \)[/tex]
- Velocity ([tex]\( v \)[/tex]) of the race car: [tex]\( 80 \, \text{m/s} \)[/tex]
2. Recall the formula for kinetic energy ([tex]\( KE \)[/tex]):
[tex]\[
KE = \frac{1}{2} m v^2
\][/tex]
3. Substitute the known values into the formula:
[tex]\[
KE = \frac{1}{2} \times 700 \, \text{kg} \times (80 \, \text{m/s})^2
\][/tex]
4. Calculate the velocity squared:
[tex]\[
(80 \, \text{m/s})^2 = 6400 \, \text{m}^2/\text{s}^2
\][/tex]
5. Multiply mass by the squared velocity:
[tex]\[
700 \, \text{kg} \times 6400 \, \text{m}^2/\text{s}^2 = 4480000 \, \text{kg} \cdot \text{m}^2/\text{s}^2
\][/tex]
6. Divide by 2 to find the kinetic energy:
[tex]\[
KE = \frac{1}{2} \times 4480000 \, \text{kg} \cdot \text{m}^2/\text{s}^2 = 2240000 \, \text{J}
\][/tex]
7. Thus, the kinetic energy of the race car is:
[tex]\[
KE = 2240000 \, \text{J} = 2.24 \times 10^6 \, \text{J}
\][/tex]
Therefore, the correct answer is option D: [tex]$2.24 \times 10^6 \, J$[/tex].
