### Understanding Velocity and Acceleration from a Quadratic EquationThe velocity of a particle is given by the equation:\[ v = 39t^2 - 93t + 47 \]where:- \( v \) is the velocity in meters per second (m/s)- \( t \) is the time in seconds (s)#### Task:Plot the velocity \( v \) and acceleration \( a \) versus time for the first 3 seconds of motion. Evaluate the velocity when acceleration \( a \) is zero. After plotting the data, answer the following questions:### Questions:1. **When \( t = 0.5 \) seconds:** - **Velocity \( v \):** \[ v = 10.25 \, \text{m/s} \] - **Acceleration \( a \):** \[ a = -73.5 \, \text{m/s}^2 \]2. **When \( t = 1.3 \) seconds:** - **Velocity \( v \):** \[ v = -7.99 \, \text{m/s} \] - **Acceleration \( a \):** \[ a = -42.3 \, \text{m/s}^2 \]3. **When \( t = 2.3 \) seconds:** - **Velocity \( v \):** \[ v = 39.41 \, \text{m/s} \] - **Acceleration \( a \):** \[ a = -3.3 \, \text{m/s}^2 \]4. **When \( a = 0 \):** - **Velocity \( v \):** \[ v = 895.6 \, \text{m/s} \]#### Graphs and Diagrams:1. **Velocity vs. Time Plot:** - Plot a graph of velocity \( v \) on the vertical axis vs. time \( t \) on the horizontal axis for \( t \) ranging from 0 to 3 seconds. - Mark the points: - \( (0.5, 10.25) \) - \( (1.3, -7.99) \) - \( (2.3, 39.41) \)2. **Acceleration vs

Drawing the velocity and acceleration versus time for the first 3 seconds of motion and calculating…

The velocity of a particle is given by v= 39t2-93t+47, where v is in meters per second and t is in seconds. Plot the velocity v and acceleration a versus time for the first 3 seconds of motion and evaluate the velocity when a is zero. Make the plots and then answer the questions. Questions: When t = 0.5 s, V= 10.25 m/s, a = i -73.5 m/s² When t = 1.3 s, V= -7.99 m/s, a = i -42.3 m/s² When t = 2.3 s, V = 39.41 m/s, a= i -3.3 m/s² When a = 0, V= i m/s 895.6

The velocity of a particle is given by v= 39t2-93t+47, where v is in meters per second and t is in seconds. Plot the velocity v and acceleration a versus time for the first 3 seconds of motion and evaluate the velocity when a is zero. Make the plots and then answer the questions. Questions: When t = 0.5 s, V= 10.25 m/s, a = i -73.5 m/s² When t = 1.3 s, V= -7.99 m/s, a = i -42.3 m/s² When t = 2.3 s, V = 39.41 m/s, a= i -3.3 m/s² When a = 0, V= i m/s 895.6

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

### Understanding Velocity and Acceleration from a Quadratic Equation

The velocity of a particle is given by the equation:

\[ v = 39t^2 - 93t + 47 \]

where:
- \( v \) is the velocity in meters per second (m/s)
- \( t \) is the time in seconds (s)

#### Task:
Plot the velocity \( v \) and acceleration \( a \) versus time for the first 3 seconds of motion. Evaluate the velocity when acceleration \( a \) is zero. After plotting the data, answer the following questions:

### Questions:

1. **When \( t = 0.5 \) seconds:**
- **Velocity \( v \):**
\[ v = 10.25 \, \text{m/s} \]
- **Acceleration \( a \):**
\[ a = -73.5 \, \text{m/s}^2 \]

2. **When \( t = 1.3 \) seconds:**
- **Velocity \( v \):**
\[ v = -7.99 \, \text{m/s} \]
- **Acceleration \( a \):**
\[ a = -42.3 \, \text{m/s}^2 \]

3. **When \( t = 2.3 \) seconds:**
- **Velocity \( v \):**
\[ v = 39.41 \, \text{m/s} \]
- **Acceleration \( a \):**
\[ a = -3.3 \, \text{m/s}^2 \]

4. **When \( a = 0 \):**
- **Velocity \( v \):**
\[ v = 895.6 \, \text{m/s} \]

#### Graphs and Diagrams:

1. **Velocity vs. Time Plot:**
- Plot a graph of velocity \( v \) on the vertical axis vs. time \( t \) on the horizontal axis for \( t \) ranging from 0 to 3 seconds.
- Mark the points:
- \( (0.5, 10.25) \)
- \( (1.3, -7.99) \)
- \( (2.3, 39.41) \)

2. **Acceleration vs

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