Kyle has a mass of [tex][tex]$54 \, \text{kg}$[/tex][/tex] and is jogging at a velocity of [tex][tex]$3 \, \text{m/s}$[/tex][/tex]. What is Kyle's kinetic energy?

(Formula: [tex]KE = \frac{1}{2}mv^2[/tex])

A. [tex]18 \, \text{J}[/tex]
B. [tex]81 \, \text{J}[/tex]
C. [tex]162 \, \text{J}[/tex]
D. [tex]243 \, \text{J}[/tex]



Answer :

To determine Kyle's kinetic energy while jogging, we can use the kinetic energy formula:

[tex]\[ KE = \frac{1}{2}mv^2 \][/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:
- The mass [tex]\( m \)[/tex] is [tex]\( 54 \, \text{kg} \)[/tex],
- The velocity [tex]\( v \)[/tex] is [tex]\( 3 \, \text{m/s} \)[/tex].

Substitute the given values into the formula:

[tex]\[ KE = \frac{1}{2} \times 54 \, \text{kg} \times (3 \, \text{m/s})^2 \][/tex]

First, calculate the square of the velocity:
[tex]\[ (3 \, \text{m/s})^2 = 9 \, \text{m}^2/\text{s}^2 \][/tex]

Next, multiply the mass by this 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]

Since the formula includes a factor of [tex]\(\frac{1}{2}\)[/tex], we need to divide this product by 2:

[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]

Therefore, Kyle's kinetic energy is:

[tex]\[ 243 \, \text{J} \][/tex]

So, the correct answer is:
[tex]\[ 243 \, \text{J} \][/tex]