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
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### 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.
Transcribed Image Text:### 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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