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Moving objects, such as automobiles, have kinetic energy (KE), which is measured in joules. This energy can be calculated using the following formula:
[tex]\[ KE = \frac{1}{2} mv^2 \][/tex]

A person drives an automobile with a mass of 450 kilograms at a velocity of 26 meters per second. The driver accelerates to a velocity of 30 meters per second.

The difference in the automobile's kinetic energy between the two velocities is [tex]\(\square\)[/tex] joules.

You may use a calculator.



Answer :

GinnyAnswer
To determine the difference in the automobile's kinetic energy between the two velocities, we will first calculate the kinetic energy at each velocity and then find the difference.

The formula for kinetic energy (KE) is:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
where [tex]\( m \)[/tex] is the mass of the automobile, and [tex]\( v \)[/tex] is its velocity.

1. Calculate the initial kinetic energy at 26 meters per second:

- Mass ([tex]\( m \)[/tex]) = 450 kilograms
- Initial velocity ([tex]\( v \)[/tex]) = 26 meters per second

Substituting the values into the formula:
[tex]\[ KE_{\text{initial}} = \frac{1}{2} \times 450 \times 26^2 \][/tex]
[tex]\[ KE_{\text{initial}} = \frac{1}{2} \times 450 \times 676 \][/tex]
[tex]\[ KE_{\text{initial}} = 0.5 \times 450 \times 676 \][/tex]
[tex]\[ KE_{\text{initial}} = 152100 \text{ joules} \][/tex]

2. Calculate the final kinetic energy at 30 meters per second:

- Mass ([tex]\( m \)[/tex]) = 450 kilograms
- Final velocity ([tex]\( v \)[/tex]) = 30 meters per second

Substituting the values into the formula:
[tex]\[ KE_{\text{final}} = \frac{1}{2} \times 450 \times 30^2 \][/tex]
[tex]\[ KE_{\text{final}} = \frac{1}{2} \times 450 \times 900 \][/tex]
[tex]\[ KE_{\text{final}} = 0.5 \times 450 \times 900 \][/tex]
[tex]\[ KE_{\text{final}} = 202500 \text{ joules} \][/tex]

3. Find the difference in kinetic energy:

[tex]\[ \Delta KE = KE_{\text{final}} - KE_{\text{initial}} \][/tex]
[tex]\[ \Delta KE = 202500 \text{ joules} - 152100 \text{ joules} \][/tex]
[tex]\[ \Delta KE = 50400 \text{ joules} \][/tex]

Therefore, the difference in the automobile's kinetic energy between the two velocities is [tex]\( 50400 \)[/tex] joules.

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