To determine Kyle's kinetic energy, we need to use the formula for kinetic energy:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
Where:
- [tex]\( KE \)[/tex] is the kinetic energy,
- [tex]\( m \)[/tex] is the mass (in kilograms),
- [tex]\( v \)[/tex] is the velocity (in meters per second).
Given:
- Kyle's mass ([tex]\( m \)[/tex]) is 54 kg,
- Kyle's velocity ([tex]\( v \)[/tex]) is 3 m/s.
Now we follow these steps:
1. Substitute the given values into the kinetic energy formula.
[tex]\[ KE = \frac{1}{2} \times 54 \, \text{kg} \times (3 \, \text{m/s})^2 \][/tex]
2. First, calculate the square of the velocity ([tex]\( 3 \, \text{m/s} \)[/tex]):
[tex]\[ (3 \, \text{m/s})^2 = 9 \, \text{m}^2/\text{s}^2 \][/tex]
3. Next, multiply the mass by the squared velocity:
[tex]\[ 54 \, \text{kg} \times 9 \, \text{m}^2/\text{s}^2 = 486 \, \text{kg} \cdot \text{m}^2/\text{s}^2 \][/tex]
4. Finally, multiply by [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[ KE = \frac{1}{2} \times 486 \, \text{kg} \cdot \text{m}^2/\text{s}^2 = 243 \, \text{kg} \cdot \text{m}^2/\text{s}^2 \][/tex]
Since the unit [tex]\( \text{kg} \cdot \text{m}^2/\text{s}^2 \)[/tex] is equal to Joules (J), the kinetic energy is:
[tex]\[ KE = 243 \, \text{J} \][/tex]
Therefore, Kyle's kinetic energy is 243 J.
