If factor assuming the speed of a Car is increased by 66%, by what it's Minimum braking distance be incrayed, Will all el else Is the same? Express C a Percent increase.

Inquiry into Physics
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ISBN:9781337515863
Author:Ostdiek
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Chapter3: Energy And Conservation Laws
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### Physics Problem Explanation

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**Problem Statement:**

"If the speed of a car is increased by 66.6% by what factor will its minimum braking distance be increased, assuming all else is the same? Express as a percent increase."

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**Key Points and Concepts:**

1. **Speed Increase:** The speed of the car is increased by 66.6%.
2. **Braking Distance:** The relationship between the speed of a car and its braking distance follows a quadratic relationship. This means that if the speed increases, the braking distance increases by the square of the speed increase factor.
3. **Percent Increase:** Expressing the increase in braking distance as a percentage.

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### Detailed Explanation:

- **Initial Speed and New Speed:**
   - Let the initial speed be `v`.
   - New speed = `v + 0.666v = 1.666v`.

- **Factors Affecting Braking Distance:**
   - Braking distance `d` is proportional to the square of the speed `v`, meaning `d ∝ v²`.
   - Therefore, the new braking distance is proportional to `(1.666v)²`.

- **Mathematical Calculation:**
   - Initial braking distance = `d ∝ v²`.
   - New braking distance = `D ∝ (1.666v)² = 2.777556v²`.

- **Percent Increase in Braking Distance:**
   - Factor by which braking distance increases = 2.777556.
   - To express as a percent increase: `(2.777556 - 1)*100% = 177.76%`.

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**Answer:**

If the speed of a car is increased by 66.6%, the minimum braking distance will increase by a factor of approximately 2.777556 or a 177.76% increase, assuming all other factors remain constant.

---

This explanation provides an in-depth understanding of the relationship between speed and braking distance and translates a practical physics problem into comprehensible steps, which can be very useful for educational purposes.
Transcribed Image Text:### Physics Problem Explanation --- **Problem Statement:** "If the speed of a car is increased by 66.6% by what factor will its minimum braking distance be increased, assuming all else is the same? Express as a percent increase." --- **Key Points and Concepts:** 1. **Speed Increase:** The speed of the car is increased by 66.6%. 2. **Braking Distance:** The relationship between the speed of a car and its braking distance follows a quadratic relationship. This means that if the speed increases, the braking distance increases by the square of the speed increase factor. 3. **Percent Increase:** Expressing the increase in braking distance as a percentage. --- ### Detailed Explanation: - **Initial Speed and New Speed:** - Let the initial speed be `v`. - New speed = `v + 0.666v = 1.666v`. - **Factors Affecting Braking Distance:** - Braking distance `d` is proportional to the square of the speed `v`, meaning `d ∝ v²`. - Therefore, the new braking distance is proportional to `(1.666v)²`. - **Mathematical Calculation:** - Initial braking distance = `d ∝ v²`. - New braking distance = `D ∝ (1.666v)² = 2.777556v²`. - **Percent Increase in Braking Distance:** - Factor by which braking distance increases = 2.777556. - To express as a percent increase: `(2.777556 - 1)*100% = 177.76%`. --- **Answer:** If the speed of a car is increased by 66.6%, the minimum braking distance will increase by a factor of approximately 2.777556 or a 177.76% increase, assuming all other factors remain constant. --- This explanation provides an in-depth understanding of the relationship between speed and braking distance and translates a practical physics problem into comprehensible steps, which can be very useful for educational purposes.
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