.What is ax at t = 12.0 s? answer in m/s^2 b. What is ax at t = 2.00 s? answer in m/s^2 c. which is the correct multiple chpoice answer attached?  d. How far does the object travel from t = 12.0 s to t = 14.0 s? answer in m

Principles of Physics: A Calculus-Based Text
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Chapter2: Motion In One Dimension
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a.What is ax at t = 12.0 s? answer in m/s^2

b. What is ax at t = 2.00 s? answer in m/s^2

c. which is the correct multiple chpoice answer attached? 

d. How far does the object travel from t = 12.0 s to t = 14.0 s? answer in m

 

 

**Velocity vs. Time Graph for an Object Moving Along the x-Axis**

The graph illustrates the velocity (\(v_x\)) of an object moving along the x-axis as a function of time (\(t\)). The velocity is measured in meters per second (m/s), while the time is measured in seconds (s).

- **Horizontal Axis (x-axis)**: Represents the time \(t\) in seconds (s), ranging from 0 to 14 seconds.
- **Vertical Axis (y-axis)**: Represents the velocity \(v_x\) in meters per second (m/s), ranging from 0 to 40 m/s.

**Description of Graph:**

1. **Time Interval from 0 to 6 seconds**: 
   - The object's velocity remains constant at 20 m/s.

2. **Time Interval from 6 to 8 seconds**: 
   - The object's velocity increases linearly from 20 m/s to 40 m/s.

3. **Time Interval from 8 to 10 seconds**: 
   - The object's velocity decreases linearly from 40 m/s to 0 m/s.

4. **Time Interval from 10 to 14 seconds**: 
   - The object's velocity remains constant at 0 m/s.

This graph effectively demonstrates how the object's motion varies over time along the x-axis, showing periods of constant velocity, acceleration, deceleration, and rest.
Transcribed Image Text:**Velocity vs. Time Graph for an Object Moving Along the x-Axis** The graph illustrates the velocity (\(v_x\)) of an object moving along the x-axis as a function of time (\(t\)). The velocity is measured in meters per second (m/s), while the time is measured in seconds (s). - **Horizontal Axis (x-axis)**: Represents the time \(t\) in seconds (s), ranging from 0 to 14 seconds. - **Vertical Axis (y-axis)**: Represents the velocity \(v_x\) in meters per second (m/s), ranging from 0 to 40 m/s. **Description of Graph:** 1. **Time Interval from 0 to 6 seconds**: - The object's velocity remains constant at 20 m/s. 2. **Time Interval from 6 to 8 seconds**: - The object's velocity increases linearly from 20 m/s to 40 m/s. 3. **Time Interval from 8 to 10 seconds**: - The object's velocity decreases linearly from 40 m/s to 0 m/s. 4. **Time Interval from 10 to 14 seconds**: - The object's velocity remains constant at 0 m/s. This graph effectively demonstrates how the object's motion varies over time along the x-axis, showing periods of constant velocity, acceleration, deceleration, and rest.
### Velocity-Time Graph Interpretation

In the context of physics education, understanding the interpretation of different graphs, particularly velocity-time graphs, is crucial. Below are four graphs depicting acceleration (\( a_x \)) as a function of time (\( t \)). Each graph contains significant information about the velocity and acceleration relationship of a moving object over time.

#### Graph Descriptions

1. **First Graph:**
   - **x-axis (Time, \( t \)):** Ranges from 0 to 15 seconds.
   - **y-axis (Acceleration, \( a_x \)):** Ranges from -10 to 10 meters per second squared (\( \text{m/s}^2 \)).
   - The acceleration varies and has distinct intervals:
     - From 0 to 6 seconds: Constant acceleration at 0 \( \text{m/s}^2 \).
     - From 6 to 12 seconds: Constant acceleration at 5 \( \text{m/s}^2 \).
     - From 12 to 15 seconds: Constant acceleration at 0 \( \text{m/s}^2 \).

2. **Second Graph:**
   - **x-axis (Time, \( t \)):** Ranges from 0 to 15 seconds.
   - **y-axis (Acceleration, \( a_x \)):** Ranges from -10 to 10 meters per second squared (\( \text{m/s}^2 \)).
   - The acceleration varies and has distinct intervals:
     - From 0 to 3 seconds: Constant acceleration at 5 \( \text{m/s}^2 \).
     - From 3 to 9 seconds: Constant acceleration at 0 \( \text{m/s}^2 \).
     - From 9 to 15 seconds: Constant acceleration at -5 \( \text{m/s}^2 \).

3. **Third Graph:**
   - **x-axis (Time, \( t \)):** Ranges from 0 to 15 seconds.
   - **y-axis (Acceleration, \( a_x \)):** Ranges from -10 to 10 meters per second squared (\( \text{m/s}^2 \)).
   - The acceleration varies and has distinct intervals:
     - From 0 to 3 seconds: Constant acceleration at -5 \( \text{m/s}^2 \).
     - From 3 to 6 seconds: Constant
Transcribed Image Text:### Velocity-Time Graph Interpretation In the context of physics education, understanding the interpretation of different graphs, particularly velocity-time graphs, is crucial. Below are four graphs depicting acceleration (\( a_x \)) as a function of time (\( t \)). Each graph contains significant information about the velocity and acceleration relationship of a moving object over time. #### Graph Descriptions 1. **First Graph:** - **x-axis (Time, \( t \)):** Ranges from 0 to 15 seconds. - **y-axis (Acceleration, \( a_x \)):** Ranges from -10 to 10 meters per second squared (\( \text{m/s}^2 \)). - The acceleration varies and has distinct intervals: - From 0 to 6 seconds: Constant acceleration at 0 \( \text{m/s}^2 \). - From 6 to 12 seconds: Constant acceleration at 5 \( \text{m/s}^2 \). - From 12 to 15 seconds: Constant acceleration at 0 \( \text{m/s}^2 \). 2. **Second Graph:** - **x-axis (Time, \( t \)):** Ranges from 0 to 15 seconds. - **y-axis (Acceleration, \( a_x \)):** Ranges from -10 to 10 meters per second squared (\( \text{m/s}^2 \)). - The acceleration varies and has distinct intervals: - From 0 to 3 seconds: Constant acceleration at 5 \( \text{m/s}^2 \). - From 3 to 9 seconds: Constant acceleration at 0 \( \text{m/s}^2 \). - From 9 to 15 seconds: Constant acceleration at -5 \( \text{m/s}^2 \). 3. **Third Graph:** - **x-axis (Time, \( t \)):** Ranges from 0 to 15 seconds. - **y-axis (Acceleration, \( a_x \)):** Ranges from -10 to 10 meters per second squared (\( \text{m/s}^2 \)). - The acceleration varies and has distinct intervals: - From 0 to 3 seconds: Constant acceleration at -5 \( \text{m/s}^2 \). - From 3 to 6 seconds: Constant
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