### Particle Motion Analysis#### Problem Statement:The position of a particle is given by the equation:\[ s = 0.23t^3 - 0.77t^2 - 2.50t + 5.65 \]where **s** is the position in feet and **t** is the time in seconds. #### Task:1. Plot the displacement (\(s\)), velocity (\(v\)), and acceleration (\(a\)) as functions of time for the first 12 seconds of motion.2. Answer the following questions based on your plots.#### Provided Diagram:- A number line depicting the position \(s\) in feet is given, indicating a range from -1 to +3 feet.#### Questions:1. **Evaluate the Velocity and Acceleration:** - **At \( t = 1.7 \) sec:** - Velocity \( v = \quad \_\_\_\_\_\_\_\_\_ \) ft/sec - Acceleration \( a = \quad \_\_\_\_\_\_\_\_\_ \) ft/sec² - **At \( t = 9.8 \) sec:** - Velocity \( v = \quad \_\_\_\_\_\_\_\_\_ \) ft/sec - Acceleration \( a = \quad \_\_\_\_\_\_\_\_\_ \) ft/sec²2. **Determine the time when the particle changes direction:** - The positive time at which the particle changes direction is \( \quad \_\_\_\_\_\_\_\_\_ \) sec.

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The position of a particle is given by s = 0.23t³ -0.77t² -2.50t + 5.65, where s is in feet and the time t is in seconds. Plot the displacement, velocity, and acceleration as functions of time for the first 12 seconds of motion. After you have the plots, answer the questions as a check on your work. -+s, ft -1 0 1 2 3 Questions: When t = 1.7 sec, V= ft/sec, ft/sec² When t = 9.8 sec, v = ft/sec, ft/sec² The positive time at which the particle changes direction is i i a = i a = sec.

The position of a particle is given by s = 0.23t³ -0.77t² -2.50t + 5.65, where s is in feet and the time t is in seconds. Plot the displacement, velocity, and acceleration as functions of time for the first 12 seconds of motion. After you have the plots, answer the questions as a check on your work. -+s, ft -1 0 1 2 3 Questions: When t = 1.7 sec, V= ft/sec, ft/sec² When t = 9.8 sec, v = ft/sec, ft/sec² The positive time at which the particle changes direction is i i a = i a = sec.

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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Question

### Particle Motion Analysis

#### Problem Statement:
The position of a particle is given by the equation:
\[ s = 0.23t^3 - 0.77t^2 - 2.50t + 5.65 \]
where **s** is the position in feet and **t** is the time in seconds.

#### Task:
1. Plot the displacement (\(s\)), velocity (\(v\)), and acceleration (\(a\)) as functions of time for the first 12 seconds of motion.
2. Answer the following questions based on your plots.

#### Provided Diagram:
- A number line depicting the position \(s\) in feet is given, indicating a range from -1 to +3 feet.

#### Questions:

1. **Evaluate the Velocity and Acceleration:**
- **At \( t = 1.7 \) sec:**
- Velocity \( v = \quad \_\_\_\_\_\_\_\_\_ \) ft/sec
- Acceleration \( a = \quad \_\_\_\_\_\_\_\_\_ \) ft/sec²

- **At \( t = 9.8 \) sec:**
- Velocity \( v = \quad \_\_\_\_\_\_\_\_\_ \) ft/sec
- Acceleration \( a = \quad \_\_\_\_\_\_\_\_\_ \) ft/sec²

2. **Determine the time when the particle changes direction:**
- The positive time at which the particle changes direction is \( \quad \_\_\_\_\_\_\_\_\_ \) sec.

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