Certainly! Let's break down the problem step-by-step:
1. Given Information:
- Mass of the automobile (\( m \)): 450 kilograms
- Velocity of the automobile (\( v \)): 26 meters per second
2. Kinetic Energy Formula:
The formula for kinetic energy (\( KE \)) is:
[tex]\[
KE = \frac{1}{2} m v^2
\][/tex]
3. Substitute the given values into the formula:
- \( m \) is 450 kilograms
- \( v \) is 26 meters per second
[tex]\[
KE = \frac{1}{2} \times 450 \times (26)^2
\][/tex]
4. Calculate the value within the parenthesis:
[tex]\[
(26)^2 = 676
\][/tex]
5. Continue with the substitution:
[tex]\[
KE = \frac{1}{2} \times 450 \times 676
\][/tex]
6. Simplify the expression:
[tex]\[
KE = 0.5 \times 450 \times 676
\][/tex]
7. Complete the multiplication:
[tex]\[
KE = 225 \times 676
\][/tex]
8. Calculate the final result:
[tex]\[
KE = 152100 \, \text{joules}
\][/tex]
Therefore, the kinetic energy of the automobile is \( 152100 \) joules when it is driven at a velocity of 26 meters per second.
If you're looking to find the difference in kinetic energy between two velocities, please provide the second velocity so we can calculate the kinetic energy for both velocities and determine the difference.
