Slove for part d e and f and h The image contains four graphs showing the relationship between position (s), velocity (v), and acceleration (a) as functions of time (t) over a period of 0 to 10 seconds. Each graph contains three curves representing these functions. Below is a detailed explanation of the graphs:1. **First Graph (Top Left):** - The vertical axis is labeled \( y \), and the horizontal axis is labeled \( t \) ranging from 0 to 10. - The position function \( s(t) \) is represented by a red curve, rising steadily. - The velocity function \( v(t) \) is shown by a black curve, rising more steeply than the position curve. - The acceleration function \( a(t) \) is depicted by a blue curve, rising less steeply than the velocity curve.2. **Second Graph (Top Right):** - The axis labels and ranges are the same as the first graph. - The position function \( s(t) \) is now shown with the blue curve. - The velocity function \( v(t) \) is represented by a black curve, which is above the other two curves and increasing rapidly. - The acceleration function \( a(t) \) is displayed as a red curve, rising in between the other two curves.3. **Third Graph (Bottom Left):** - Again, the axis labels and ranges are consistent with the previous graphs. - Velocity \( v(t) \) is represented by a purple curve rising gradually. - Position \( s(t) \) is shown by a blue curve, which rises more steeply. - Acceleration \( a(t) \) is depicted by a red curve, increasing more rapidly compared to velocity.4. **Fourth Graph (Bottom Right):** - Axis labels and scales remain the same. - The position function \( s(t) \) is shown by a blue curve that rises steeply. - Acceleration \( a(t) \) is represented by a black curve, rising less steeply than the position curve but more than the velocity. - The velocity function \( v(t) \) is depicted by a red curve, rising in between the position and acceleration curves.**Question (h):** The problem asks: "When, for \( 0 \leq t < \infty \), is the particle speeding up?" You are instructed to enter your A particle moves according to a law of motion \( s = f(t) \), \( t \geq 0 \), where \( t \) is measured in seconds and \( s \) in feet.\[ f(t) = 0.01t^4 - 0.03t^3 \](a) **Find the velocity at time \( t \) (in ft/s).**\[ v(t) = 0.04t^3 - 0.09t^2 \]✓(b) **What is the velocity after 1 second(s)?**\[ v(1) = -0.05 \, \text{ft/s} \](c) **When is the particle at rest?**- Smaller value \( t = 0 \, \text{s} \) ✓- Larger value \( t = 2.25 \, \text{s} \) ✓(d) **When is the particle moving in the positive direction?** (Enter your answer using interval notation.)Incorrect attempt:\[ t > 2.25 \]✗(e) **Find the total distance traveled during the first 9 seconds.** (Round your answer to two decimal places.)Incorrect attempt:\[ 43.74 \]✗(f) **Find the acceleration at time \( t \) (in ft/s\(^2\)).**Incorrect attempt:\[ a(t) = 0.06 \]✗**Find the acceleration after 1 second(s).**\[ a(1) = \, \_\_\_\_ \text{ft/s}^2 \]

Answered: Image /qna-images/answer/d31d9877-10d5-4379-a08d-29c0e76b7243.jpg

8 https://www.webassign.net/web/Student/Assignment-Responses/submit?dep=270589368tags=autosave&question4708001 0 19) Graph the position, velocity, and acceleration functions for the first 9 seconds. 40 40 30 30 20 20 10 10 2 4 8 10 2 4 6 8 10 y 40 40 30 30 20 20 10 10 t 10 2. 4. 6. 8 2 4. 6. 8. 10 (h) When, for 0 st<, is the particle speeding up? (Enter your answer using interval notation.) PType here to search

8 https://www.webassign.net/web/Student/Assignment-Responses/submit?dep=270589368tags=autosave&question4708001 0 19) Graph the position, velocity, and acceleration functions for the first 9 seconds. 40 40 30 30 20 20 10 10 2 4 8 10 2 4 6 8 10 y 40 40 30 30 20 20 10 10 t 10 2. 4. 6. 8 2 4. 6. 8. 10 (h) When, for 0 st<, is the particle speeding up? (Enter your answer using interval notation.) PType here to search

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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Question

Slove for part d e and f and h

The image contains four graphs showing the relationship between position (s), velocity (v), and acceleration (a) as functions of time (t) over a period of 0 to 10 seconds. Each graph contains three curves representing these functions. Below is a detailed explanation of the graphs:

1. **First Graph (Top Left):**
- The vertical axis is labeled \( y \), and the horizontal axis is labeled \( t \) ranging from 0 to 10.
- The position function \( s(t) \) is represented by a red curve, rising steadily.
- The velocity function \( v(t) \) is shown by a black curve, rising more steeply than the position curve.
- The acceleration function \( a(t) \) is depicted by a blue curve, rising less steeply than the velocity curve.

2. **Second Graph (Top Right):**
- The axis labels and ranges are the same as the first graph.
- The position function \( s(t) \) is now shown with the blue curve.
- The velocity function \( v(t) \) is represented by a black curve, which is above the other two curves and increasing rapidly.
- The acceleration function \( a(t) \) is displayed as a red curve, rising in between the other two curves.

3. **Third Graph (Bottom Left):**
- Again, the axis labels and ranges are consistent with the previous graphs.
- Velocity \( v(t) \) is represented by a purple curve rising gradually.
- Position \( s(t) \) is shown by a blue curve, which rises more steeply.
- Acceleration \( a(t) \) is depicted by a red curve, increasing more rapidly compared to velocity.

4. **Fourth Graph (Bottom Right):**
- Axis labels and scales remain the same.
- The position function \( s(t) \) is shown by a blue curve that rises steeply.
- Acceleration \( a(t) \) is represented by a black curve, rising less steeply than the position curve but more than the velocity.
- The velocity function \( v(t) \) is depicted by a red curve, rising in between the position and acceleration curves.

**Question (h):** The problem asks: "When, for \( 0 \leq t < \infty \), is the particle speeding up?" You are instructed to enter your

A particle moves according to a law of motion \( s = f(t) \), \( t \geq 0 \), where \( t \) is measured in seconds and \( s \) in feet.

\[ f(t) = 0.01t^4 - 0.03t^3 \]

(a) **Find the velocity at time \( t \) (in ft/s).**

\[ v(t) = 0.04t^3 - 0.09t^2 \]

✓

(b) **What is the velocity after 1 second(s)?**

\[ v(1) = -0.05 \, \text{ft/s} \]

(c) **When is the particle at rest?**

- Smaller value \( t = 0 \, \text{s} \) ✓
- Larger value \( t = 2.25 \, \text{s} \) ✓

(d) **When is the particle moving in the positive direction?** (Enter your answer using interval notation.)

Incorrect attempt:

\[ t > 2.25 \]

✗

(e) **Find the total distance traveled during the first 9 seconds.** (Round your answer to two decimal places.)

Incorrect attempt:

\[ 43.74 \]

✗

(f) **Find the acceleration at time \( t \) (in ft/s\(^2\)).**

Incorrect attempt:

\[ a(t) = 0.06 \]

✗

**Find the acceleration after 1 second(s).**

\[ a(1) = \, \_\_\_\_ \text{ft/s}^2 \]

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