To determine the kinetic energy of a 25-gram bullet traveling at [tex]\( 500 \, \text{m/s} \)[/tex], follow these steps:
1. Convert the mass of the bullet to kilograms:
The mass of the bullet is given as 25 grams. Since 1 gram is equal to 0.001 kilograms, we convert the mass to kilograms:
[tex]\[
\text{Mass in kilograms} = 25 \, \text{grams} \times 0.001 \, \frac{\text{kilograms}}{\text{gram}} = 0.025 \, \text{kg}
\][/tex]
2. Identify the velocity of the bullet:
The velocity is given as [tex]\( 500 \, \text{m/s} \)[/tex].
3. Use the formula for kinetic energy:
The formula to calculate kinetic energy ([tex]\( KE \)[/tex]) is:
[tex]\[
KE = \frac{1}{2} \times \text{mass} \times \text{velocity}^2
\][/tex]
4. Substitute the values into the kinetic energy formula:
Plug in the mass ([tex]\( 0.025 \, \text{kg} \)[/tex]) and velocity ([tex]\( 500 \, \text{m/s} \)[/tex]):
[tex]\[
KE = \frac{1}{2} \times 0.025 \, \text{kg} \times (500 \, \text{m/s})^2
\][/tex]
5. Calculate the squared velocity:
First, square the velocity:
[tex]\[
(500 \, \text{m/s})^2 = 250000 \, \text{(m/s)}^2
\][/tex]
6. Multiply the mass by the squared velocity:
[tex]\[
0.025 \, \text{kg} \times 250000 \, \text{(m/s)}^2 = 6250 \, \text{kg} \cdot \text{m}^2/\text{s}^2
\][/tex]
7. Multiply by [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
KE = \frac{1}{2} \times 6250 \, \text{kg} \cdot \text{m}^2/\text{s}^2 = 3125 \, \text{J}
\][/tex]
Therefore, the kinetic energy of the 25-gram bullet traveling at [tex]\( 500 \, \text{m/s} \)[/tex] is [tex]\( 3125 \, \text{J} \)[/tex].
