A student is speeding down Highway 16 in her fancy red Porsche when her radar system warns her of an obstacle 400 feet ahead. She immediately applies the brakes, starts to slow down, and spots a skunk in the road directly ahead of her. The "black box" in the Porsche records the car's speed every two seconds, producing the following table. The speed decreases throughout the 10 seconds it takes to stop, although not necessarily at a uniform rate. Time since brakes applied (sec) 0 2 4 6 8 10 Speed (ft/sec) 105 85 55 20 15 0 A. What is your best estimate of the total distance the student's car traveled before coming to rest (note that the best estimate is probably not the over or under estimate that you can most easily find, use the trapezoidal approximation)? distance = B. Given the fact that the Porsche slows down during breaking, give a sharp i. underestimate of the distance traveled: ii. overestimate of the distance traveled: C. Which one of the following statements can you justify from the information given? OA. The "black box" data is inconclusive. The skunk may or may not have been hit. OB. The car stopped before getting to the skunk. O C. The skunk was hit by the car.
A student is speeding down Highway 16 in her fancy red Porsche when her radar system warns her of an obstacle 400 feet ahead. She immediately applies the brakes, starts to slow down, and spots a skunk in the road directly ahead of her. The "black box" in the Porsche records the car's speed every two seconds, producing the following table. The speed decreases throughout the 10 seconds it takes to stop, although not necessarily at a uniform rate. Time since brakes applied (sec) 0 2 4 6 8 10 Speed (ft/sec) 105 85 55 20 15 0 A. What is your best estimate of the total distance the student's car traveled before coming to rest (note that the best estimate is probably not the over or under estimate that you can most easily find, use the trapezoidal approximation)? distance = B. Given the fact that the Porsche slows down during breaking, give a sharp i. underestimate of the distance traveled: ii. overestimate of the distance traveled: C. Which one of the following statements can you justify from the information given? OA. The "black box" data is inconclusive. The skunk may or may not have been hit. OB. The car stopped before getting to the skunk. O C. The skunk was hit by the car.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Extra Problem**
A student is speeding down Highway 16 in her fancy red Porsche when her radar system warns her of an obstacle 400 feet ahead. She immediately applies the brakes, starts to slow down, and spots a skunk in the road directly ahead of her. The "black box" in the Porsche records the car's speed every two seconds, producing the following table. The speed decreases throughout the 10 seconds it takes to stop, although not necessarily at a uniform rate.
| Time since brakes applied (sec) | 0 | 2 | 4 | 6 | 8 | 10 |
|----------------------------------|---|---|---|---|---|----|
| Speed (ft/sec) | 105 | 85 | 55 | 20 | 15 | 0 |
**A. What is your best estimate of the total distance the student’s car traveled before coming to a rest?**
(Note that the best estimate is probably not the over or under estimate that you can most easily find, use the trapezoidal approximation.)
**B. Given the fact that the Porsche slows down during braking, give a sharp**
- **i. underestimate of the distance traveled**: [ ]
- **ii. overestimate of the distance traveled**: [ ]
**C. Which one of the following statements can you justify from the information given?**
- **A. The “black box” data is inconclusive. The skunk may or may not have been hit.**
- **B. The car stopped before getting to the skunk.**
- **C. The skunk was hit by the car.**
#### Explanation of the table and diagram for educational purposes:
The table provided records data on how the car's speed changes over a 10-second period. The first row lists the time in seconds since the brakes were applied, starting from 0 seconds (when the brakes were first applied) to 10 seconds (when the car comes to a complete stop). The second row lists the corresponding speeds of the car in feet per second at each time interval.
To estimate the total distance traveled, one could calculate the area under the speed-time graph represented by this table. This estimation can be derived using the trapezoidal rule. This numerical method estimates the area under a curve by summing the areas of trapezoids under the graph of the function (speed in this case).
For a more accurate understanding and calculation, students](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe8fabc15-e5db-480c-94d9-e42b67b656a8%2Fe7d87f1f-a684-4522-84a1-d55589dfbead%2Fukf69ld_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Extra Problem**
A student is speeding down Highway 16 in her fancy red Porsche when her radar system warns her of an obstacle 400 feet ahead. She immediately applies the brakes, starts to slow down, and spots a skunk in the road directly ahead of her. The "black box" in the Porsche records the car's speed every two seconds, producing the following table. The speed decreases throughout the 10 seconds it takes to stop, although not necessarily at a uniform rate.
| Time since brakes applied (sec) | 0 | 2 | 4 | 6 | 8 | 10 |
|----------------------------------|---|---|---|---|---|----|
| Speed (ft/sec) | 105 | 85 | 55 | 20 | 15 | 0 |
**A. What is your best estimate of the total distance the student’s car traveled before coming to a rest?**
(Note that the best estimate is probably not the over or under estimate that you can most easily find, use the trapezoidal approximation.)
**B. Given the fact that the Porsche slows down during braking, give a sharp**
- **i. underestimate of the distance traveled**: [ ]
- **ii. overestimate of the distance traveled**: [ ]
**C. Which one of the following statements can you justify from the information given?**
- **A. The “black box” data is inconclusive. The skunk may or may not have been hit.**
- **B. The car stopped before getting to the skunk.**
- **C. The skunk was hit by the car.**
#### Explanation of the table and diagram for educational purposes:
The table provided records data on how the car's speed changes over a 10-second period. The first row lists the time in seconds since the brakes were applied, starting from 0 seconds (when the brakes were first applied) to 10 seconds (when the car comes to a complete stop). The second row lists the corresponding speeds of the car in feet per second at each time interval.
To estimate the total distance traveled, one could calculate the area under the speed-time graph represented by this table. This estimation can be derived using the trapezoidal rule. This numerical method estimates the area under a curve by summing the areas of trapezoids under the graph of the function (speed in this case).
For a more accurate understanding and calculation, students
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