The number of feet that a car travels before stopping depends on the driver's reaction time and the braking distance, as shown below. For one driver, the stopping distance is given by the polynomial function\[ f(v) = 0.03v^2 + 0.4v \]where $ v $ is the velocity of the car. Find the stopping distance when the driver is traveling at 30 mph.\[ \boxed{} \text{ft} \]**Explanation of Diagram:**The diagram illustrates the stopping process of a car, which is divided into two main phases:1. **Reaction Time:** - This is the distance the car travels from the moment the driver decides to stop (shown by the caption "Decision to stop") to the moment the brakes are applied. This period is characterized by the driver’s reaction time. 2. **Braking Distance:** - This is the distance the car travels from the moment the brakes are applied until the car comes to a complete stop. It’s indicated by the red arrow.**Overall Stopping Distance ($ d $):**- The total stopping distance is the sum of the distances covered during the reaction time and the braking distance. It is shown as a blue arrow spanning from the beginning of the reaction time to where the car completely stops.There is also an image showing a police officer or traffic authority figure, which seems to be contextually related to the importance of understanding stopping distances for safety and legal reasons. This image reinforces the educational point by emphasizing real-world application and the importance of adhering to safety measures.

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The number of feet that a car travels before stopping depends on the driver's reaction time and the braking distance, as shown below. For one driver, the stopping distance is given by the polynomial function f(v) = 0.03v² + 0.4v where v is the velocity of the car. Find the stopping distance when the driver is traveling at 30 mph. ft Stopping distance d Reaction time Braking distance Decision to stop Robert E. Daemmrich/Getty Images

The number of feet that a car travels before stopping depends on the driver's reaction time and the braking distance, as shown below. For one driver, the stopping distance is given by the polynomial function f(v) = 0.03v² + 0.4v where v is the velocity of the car. Find the stopping distance when the driver is traveling at 30 mph. ft Stopping distance d Reaction time Braking distance Decision to stop Robert E. Daemmrich/Getty Images

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.

Question

The number of feet that a car travels before stopping depends on the driver's reaction time and the braking distance, as shown below. For one driver, the stopping distance is given by the polynomial function

\[ f(v) = 0.03v^2 + 0.4v \]

where $ v $ is the velocity of the car. Find the stopping distance when the driver is traveling at 30 mph.

\[ \boxed{} \text{ft} \]

**Explanation of Diagram:**

The diagram illustrates the stopping process of a car, which is divided into two main phases:

1. **Reaction Time:**
- This is the distance the car travels from the moment the driver decides to stop (shown by the caption "Decision to stop") to the moment the brakes are applied. This period is characterized by the driver’s reaction time.

2. **Braking Distance:**
- This is the distance the car travels from the moment the brakes are applied until the car comes to a complete stop. It’s indicated by the red arrow.

**Overall Stopping Distance ($ d $):**
- The total stopping distance is the sum of the distances covered during the reaction time and the braking distance. It is shown as a blue arrow spanning from the beginning of the reaction time to where the car completely stops.

There is also an image showing a police officer or traffic authority figure, which seems to be contextually related to the importance of understanding stopping distances for safety and legal reasons. This image reinforces the educational point by emphasizing real-world application and the importance of adhering to safety measures.

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