please write ✍️ clean and readable Hello! I need your help ASAP. Please look at my calculus questions about velocity and average. I had attached the questions below. (Note please answer ALL questions 1-8) * in the pictures below it doesn't show number 8. So I will type that question here ? Question 8). From 3 hrs to 4 hrs , what is the sign of the velocity and sign of acceleration? What is the happening in that time interval. Thank you **Velocity and Acceleration Analysis****3. Over what interval(s) of time is velocity negative? What does this mean in this scenario?****4. Over what interval(s) of time is velocity positive? What does this mean in this scenario?****5. What time(s) is velocity zero and what is happening then?****6. Find the acceleration function.****7. From 4 hours to 5 hours, what is the sign of velocity and sign of acceleration? What is happening in that time interval?** **The Situation:** We will begin time at the moment you leave your classroom on campus. The classroom is 5 miles from your home. You are tired since you just finished taking your calculus test and you pedal your bicycle in the opposite direction from home for a while. Later you turn around and head toward home again, but since you are dehydrated, you end up turning around again a short time later. After 5 hours you stop.Let $ s(t) $ be your distance (in miles) from home at time $ t $ (hours).\[ s(t) = t^3 - 8t^2 + 16t + 5 \]This position function is graphed next and linked in Desmos for your convenience.**Graph Explanation:**- The graph displays the function $ s(t) = t^3 - 8t^2 + 16t + 5 $, showing the distance from home over time (hours) on a coordinate plane.- The x-axis represents time $ t $ in hours, ranging from 0 to 5 hours.- The y-axis represents distance from home in miles.- The curve illustrates the changes in distance over time as you bicycle back and forth.**Task:**1. Find and interpret $ s(0) $ and $ s(5) $. Be sure to use measurement units. Label these points on the graph.

Answered: 3. Over what interval(s) of time is…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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please write ✍️ clean and readable

Hello! I need your help ASAP. Please look at my calculus questions about velocity and average. I had attached the questions below. (Note please answer ALL questions 1-8)

* in the pictures below it doesn't show number 8. So I will type that question here ?

Question 8). From 3 hrs to 4 hrs , what is the sign of the velocity and sign of acceleration? What is the happening in that time interval.

Thank you

**Velocity and Acceleration Analysis**

**3. Over what interval(s) of time is velocity negative? What does this mean in this scenario?**

**4. Over what interval(s) of time is velocity positive? What does this mean in this scenario?**

**5. What time(s) is velocity zero and what is happening then?**

**6. Find the acceleration function.**

**7. From 4 hours to 5 hours, what is the sign of velocity and sign of acceleration? What is happening in that time interval?**

**The Situation:** We will begin time at the moment you leave your classroom on campus. The classroom is 5 miles from your home. You are tired since you just finished taking your calculus test and you pedal your bicycle in the opposite direction from home for a while. Later you turn around and head toward home again, but since you are dehydrated, you end up turning around again a short time later. After 5 hours you stop.

Let $ s(t) $ be your distance (in miles) from home at time $ t $ (hours).

\[ s(t) = t^3 - 8t^2 + 16t + 5 \]

This position function is graphed next and linked in Desmos for your convenience.

**Graph Explanation:**

- The graph displays the function $ s(t) = t^3 - 8t^2 + 16t + 5 $, showing the distance from home over time (hours) on a coordinate plane.
- The x-axis represents time $ t $ in hours, ranging from 0 to 5 hours.
- The y-axis represents distance from home in miles.
- The curve illustrates the changes in distance over time as you bicycle back and forth.

**Task:**

1. Find and interpret $ s(0) $ and $ s(5) $. Be sure to use measurement units. Label these points on the graph.

Expert Solution

Step 1: Part (1) - Finding the value of s(0) and s(5) and plotting in the graph:

“Since you have posted a question with multiple sub parts, we will provide the solution only to the first three sub parts as per our Q&A guidelines. Please repost the remaining sub parts separately.”

$The space distance space function space is space given space by comma straight s left parenthesis straight t right parenthesis space equals space straight t cubed space minus space 8 straight t squared space plus space 16 straight t space plus space 5 Putting space straight t space equals space 0 comma straight s left parenthesis 0 right parenthesis space equals space space 0 cubed space minus space 8 left parenthesis 0 right parenthesis squared space plus space 16 left parenthesis 0 right parenthesis space plus space 5 space straight s left parenthesis 0 right parenthesis space equals space 5 space miles Putting space straight t space equals space 5 comma straight s left parenthesis 5 right parenthesis space equals space space left parenthesis 5 right parenthesis cubed space minus space 8 left parenthesis 5 right parenthesis squared space plus space 16 left parenthesis 5 right parenthesis space plus space 5 straight s left parenthesis 5 right parenthesis space equals space 125 space minus space 200 space plus space 80 space plus space 5 space equals space 210 space minus space 200 straight s left parenthesis 5 right parenthesis space equals space 10 space miles$

Plotting the points in the graph:

The points are (0, 5) and (5, 10).