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What is the kinetic energy of a [tex][tex]$700 \, \text{kg}$[/tex][/tex] race car that has a velocity of [tex][tex]$80 \, \text{m/s}$[/tex][/tex]?

A. [tex][tex]$8.75 \, \text{J}$[/tex][/tex]
B. [tex][tex]$3.36 \times 10^4 \, \text{J}$[/tex][/tex]
C. [tex][tex]$5.49 \times 10^4 \, \text{J}$[/tex][/tex]
D. [tex][tex]$2.24 \times 10^6 \, \text{J}$[/tex][/tex]


Sagot :

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].