Certainly! To calculate the kinetic energy of an object in motion, we use the formula:
[tex]\[ k = \frac{1}{2} m v^2 \][/tex]
where:
- [tex]\( k \)[/tex] is the kinetic energy,
- [tex]\( m \)[/tex] is the mass of the object, and
- [tex]\( v \)[/tex] is the velocity of the object.
Let's follow the steps to find the kinetic energy.
### Step-by-Step Solution:
1. Identify the values given:
- Mass [tex]\( m = 45 \)[/tex] kilograms
- Velocity [tex]\( v = 3 \)[/tex] meters per second
2. Substitute the values into the formula:
[tex]\[ k = \frac{1}{2} \times 45 \times (3)^2 \][/tex]
3. Calculate the square of the velocity:
[tex]\[ (3)^2 = 9 \][/tex]
4. Continue substituting this value into the formula:
[tex]\[ k = \frac{1}{2} \times 45 \times 9 \][/tex]
5. Multiply the mass by the square of the velocity:
[tex]\[ 45 \times 9 = 405 \][/tex]
6. Multiply this result by [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[ \frac{1}{2} \times 405 = 202.5 \][/tex]
So, the kinetic energy [tex]\( k \)[/tex] of a 45-kilogram object traveling at 3 meters per second is:
[tex]\[ k = 202.5 \text{ Joules} \][/tex]
Therefore, the kinetic energy of the object is 202.5 Joules.
