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Answer :
To solve this problem, we'll use the principles of work and energy. The main idea is that the work done by the brakes is equal to the change in the car's kinetic energy.
Here’s how we can figure it out step-by-step:
1. Initial Information:
- Mass of the car ([tex]\(m\)[/tex]) = 1200 kg
- Initial velocity of the car ([tex]\(v\)[/tex]) = 25 m/s
- Braking force ([tex]\(F\)[/tex]) = 8000 N
2. Concepts Used:
- The work done by the brakes is the force multiplied by the distance ([tex]\(d\)[/tex]) the car travels before coming to a stop.
- Work done is also equivalent to the change in kinetic energy.
3. Calculating Initial Kinetic Energy:
- The initial kinetic energy ([tex]\(\text{KE}_{\text{initial}}\)[/tex]) is given by the formula:
[tex]\[
\text{KE}_{\text{initial}} = \frac{1}{2} m v^2
\][/tex]
- Substituting the known values:
[tex]\[
\text{KE}_{\text{initial}} = \frac{1}{2} \times 1200 \times 25^2 = 375000 \, \text{Joules}
\][/tex]
4. Work-Energy Principle:
- The work done by the brakes ([tex]\(\text{Work}\)[/tex]) = Force [tex]\(\times\)[/tex] Distance
- Since the car stops, all the initial kinetic energy is transformed into the work done by the brakes to stop the car.
- Therefore:
[tex]\[
\text{Work} = \text{KE}_{\text{initial}}
\][/tex]
- Substituting, we have:
[tex]\[
8000 \times d = 375000
\][/tex]
5. Solve for Distance ([tex]\(d\)[/tex]):
- Rearranging the formula to solve for [tex]\(d\)[/tex]:
[tex]\[
d = \frac{375000}{8000} = 46.875 \, \text{meters}
\][/tex]
Therefore, the car travels approximately 46.9 meters before it comes to a stop. The correct answer to the given options is 46.9 m.
Here’s how we can figure it out step-by-step:
1. Initial Information:
- Mass of the car ([tex]\(m\)[/tex]) = 1200 kg
- Initial velocity of the car ([tex]\(v\)[/tex]) = 25 m/s
- Braking force ([tex]\(F\)[/tex]) = 8000 N
2. Concepts Used:
- The work done by the brakes is the force multiplied by the distance ([tex]\(d\)[/tex]) the car travels before coming to a stop.
- Work done is also equivalent to the change in kinetic energy.
3. Calculating Initial Kinetic Energy:
- The initial kinetic energy ([tex]\(\text{KE}_{\text{initial}}\)[/tex]) is given by the formula:
[tex]\[
\text{KE}_{\text{initial}} = \frac{1}{2} m v^2
\][/tex]
- Substituting the known values:
[tex]\[
\text{KE}_{\text{initial}} = \frac{1}{2} \times 1200 \times 25^2 = 375000 \, \text{Joules}
\][/tex]
4. Work-Energy Principle:
- The work done by the brakes ([tex]\(\text{Work}\)[/tex]) = Force [tex]\(\times\)[/tex] Distance
- Since the car stops, all the initial kinetic energy is transformed into the work done by the brakes to stop the car.
- Therefore:
[tex]\[
\text{Work} = \text{KE}_{\text{initial}}
\][/tex]
- Substituting, we have:
[tex]\[
8000 \times d = 375000
\][/tex]
5. Solve for Distance ([tex]\(d\)[/tex]):
- Rearranging the formula to solve for [tex]\(d\)[/tex]:
[tex]\[
d = \frac{375000}{8000} = 46.875 \, \text{meters}
\][/tex]
Therefore, the car travels approximately 46.9 meters before it comes to a stop. The correct answer to the given options is 46.9 m.
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