An automotive engineer is testing how quickly a newly designed sports car accelerates from rest. He has collected data giving the velocity V, in miles per hour, as a function of time t, in seconds, since the car was at rest. Below is a table giving a portion of his data. Time (t) Velocity (V) 2.0 28.4 2.5 33.9 3.0 39.4 3.5 44.9 (a) By calculating differences, show that the data in this table can be modeled by a linear function. Time 2.0 to 2.5 2.5 to 3.0 3.0 to 3.5 Change in t Change in V (b) What is the slope for the linear function modeling velocity as a function of time? mph per sec Explain in practical terms the meaning of the slope. This means that, after every second, the car will be going miles per hour faster. This says that the acceleration is ---Select--- varying constant . (c) Use the data in the table to find the formula for velocity V as a linear function of time t that is valid over the time period covered in the table. V =
An automotive engineer is testing how quickly a newly designed sports car accelerates from rest. He has collected data giving the velocity V, in miles per hour, as a function of time t, in seconds, since the car was at rest. Below is a table giving a portion of his data. Time (t) Velocity (V) 2.0 28.4 2.5 33.9 3.0 39.4 3.5 44.9 (a) By calculating differences, show that the data in this table can be modeled by a linear function. Time 2.0 to 2.5 2.5 to 3.0 3.0 to 3.5 Change in t Change in V (b) What is the slope for the linear function modeling velocity as a function of time? mph per sec Explain in practical terms the meaning of the slope. This means that, after every second, the car will be going miles per hour faster. This says that the acceleration is ---Select--- varying constant . (c) Use the data in the table to find the formula for velocity V as a linear function of time t that is valid over the time period covered in the table. V =
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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An automotive engineer is testing how quickly a newly designed sports car accelerates from rest. He has collected data giving the velocity V, in miles per hour, as a function of time t, in seconds, since the car was at rest. Below is a table giving a portion of his data.
| Time (t) | Velocity (V) |
|---|---|
| 2.0 | 28.4 |
| 2.5 | 33.9 |
| 3.0 | 39.4 |
| 3.5 | 44.9 |
(a) By calculating differences, show that the data in this table can be modeled by a linear function.
(b) What is the slope for the linear function modeling velocity as a function of time?
mph per sec
Explain in practical terms the meaning of the slope.
(c) Use the data in the table to find the formula for velocity V as a linear function of time t that is valid over the time period covered in the table.
V =
(d) What would your formula from part (c) give for velocity of the car at time 0?
V(0) =
What does this say about the validity of the linear formula over the initial segment of the experiment? Explain your answer in practical terms.
(e) Assume that the linear formula you found in part (c) is valid from 2 seconds through 5 seconds. The marketing department wants to know from the engineer how to complete the following statement: "This car goes from 0 to 60 mph in ____ seconds." How should they fill in the blank? (Round your answer to two decimal places.)
| Time | 2.0 to 2.5 | 2.5 to 3.0 | 3.0 to 3.5 |
|---|---|---|---|
| Change in t | |||
| Change in V |
(b) What is the slope for the linear function modeling velocity as a function of time?
mph per sec
Explain in practical terms the meaning of the slope.
This means that, after every second, the car will be going miles per hour faster. This says that the acceleration is ---Select--- varying constant .
(c) Use the data in the table to find the formula for velocity V as a linear function of time t that is valid over the time period covered in the table.
V =
V(0) =
What does this say about the validity of the linear formula over the initial segment of the experiment? Explain your answer in practical terms.
This answer has not been graded yet.
(e) Assume that the linear formula you found in part (c) is valid from 2 seconds through 5 seconds. The marketing department wants to know from the engineer how to complete the following statement: "This car goes from 0 to 60 mph in ____ seconds." How should they fill in the blank? (Round your answer to two decimal places.)
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