let s(t) = 9f² + 2€ + 80 be the position in miles of a car driving at tinct in hars. The cars velocity at any time it is given by u(t)= 18€+2 find the cars position when the car is going 38 mph.
let s(t) = 9f² + 2€ + 80 be the position in miles of a car driving at tinct in hars. The cars velocity at any time it is given by u(t)= 18€+2 find the cars position when the car is going 38 mph.
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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![**Understanding Position and Velocity Functions:**
In this exercise, we are given the position and velocity functions of a car over time and need to determine the car's position when it is moving at a specific speed.
1. **Position Function:**
The position of the car, \(S(t)\), in miles, at any time \(t\) in hours is given by:
\[
S(t) = 9t^2 + 2t + 80
\]
2. **Velocity Function:**
The velocity of the car, \(v(t)\), in miles per hour (mph), at any time \(t\) is given by:
\[
v(t) = 18t + 2
\]
3. **Problem:**
Find the position of the car when it is traveling at 38 mph.
### Steps to Solve:
### Step 1: Set the velocity function equal to 38 mph
To find the time \(t\) when the car is traveling at 38 mph, set the velocity function \(v(t)\) to 38 and solve for \(t\).
\[
18t + 2 = 38
\]
\[
18t = 36
\]
\[
t = 2 \text{ hours}
\]
### Step 2: Find the position at \(t = 2\) hours
Substitute \(t = 2\) into the position function \(S(t)\):
\[
S(2) = 9(2)^2 + 2(2) + 80
\]
\[
S(2) = 9(4) + 4 + 80
\]
\[
S(2) = 36 + 4 + 80
\]
\[
S(2) = 120 \text{ miles}
\]
Therefore, the position of the car when it is traveling at 38 mph is **120 miles**.
Using these steps, you can understand how to analyze and solve problems involving position and velocity functions in calculus.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F77ed505d-a3a4-461d-a128-f231a57c9aac%2F309be927-b54a-4624-9715-61a0bef442c0%2Fdf5ne3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Understanding Position and Velocity Functions:**
In this exercise, we are given the position and velocity functions of a car over time and need to determine the car's position when it is moving at a specific speed.
1. **Position Function:**
The position of the car, \(S(t)\), in miles, at any time \(t\) in hours is given by:
\[
S(t) = 9t^2 + 2t + 80
\]
2. **Velocity Function:**
The velocity of the car, \(v(t)\), in miles per hour (mph), at any time \(t\) is given by:
\[
v(t) = 18t + 2
\]
3. **Problem:**
Find the position of the car when it is traveling at 38 mph.
### Steps to Solve:
### Step 1: Set the velocity function equal to 38 mph
To find the time \(t\) when the car is traveling at 38 mph, set the velocity function \(v(t)\) to 38 and solve for \(t\).
\[
18t + 2 = 38
\]
\[
18t = 36
\]
\[
t = 2 \text{ hours}
\]
### Step 2: Find the position at \(t = 2\) hours
Substitute \(t = 2\) into the position function \(S(t)\):
\[
S(2) = 9(2)^2 + 2(2) + 80
\]
\[
S(2) = 9(4) + 4 + 80
\]
\[
S(2) = 36 + 4 + 80
\]
\[
S(2) = 120 \text{ miles}
\]
Therefore, the position of the car when it is traveling at 38 mph is **120 miles**.
Using these steps, you can understand how to analyze and solve problems involving position and velocity functions in calculus.
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