For this problem, assume the values on the axes of the graph have 1 decimal place of precision when measured. An athlete is training on a 100 m long linear track. His motion is described by the graph of his position vs. time, below.

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Chapter1: Units, Trigonometry. And Vectors
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For this problem, assume the values on the axes of the graph have 1 decimal place of precision when measured.

An athlete is training on a 100 m long linear track. His motion is described by the graph of his position vs. time, below.

 

### Understanding Velocity in Graph Segments

#### (a) Segment Analysis

For each segment of the graph, determine the athlete’s velocity magnitude and direction:

- **Segment A:**
  - **Magnitude \( v_A \):** Input is 4.0 m/s, marked as incorrect.
  - **Direction \( v_A \):** Positive x, marked as correct.

- **Segment B:**
  - **Magnitude \( v_B \):** Input is 0 m/s, marked as correct.
  - **Direction \( v_B \):** The magnitude is zero, marked as correct.

- **Segment C:**
  - **Magnitude \( v_C \):** Input is 4.0 m/s, marked as incorrect.
  - **Direction \( v_C \):** Negative x, marked as correct.

- **Segment D:**
  - **Magnitude \( v_D \):** Input is 4.0 m/s, marked as incorrect.
  - **Direction \( v_D \):** Positive x, marked as correct.

#### (b) Average Velocity

Calculate the athlete's average velocity over a 60-second interval:

- **Magnitude:** Input is 4.0 m/s, marked as incorrect.
- **Direction:** Positive x, marked as correct.

### Explanation

This exercise focuses on analyzing segments of a velocity graph. Errors in magnitude indicate a need for reevaluation of calculations based on the graph details. Understanding zero magnitude in segment B helps interpret periods of rest. The correct direction selections guide comprehension of directional changes throughout the athlete's movement.
Transcribed Image Text:### Understanding Velocity in Graph Segments #### (a) Segment Analysis For each segment of the graph, determine the athlete’s velocity magnitude and direction: - **Segment A:** - **Magnitude \( v_A \):** Input is 4.0 m/s, marked as incorrect. - **Direction \( v_A \):** Positive x, marked as correct. - **Segment B:** - **Magnitude \( v_B \):** Input is 0 m/s, marked as correct. - **Direction \( v_B \):** The magnitude is zero, marked as correct. - **Segment C:** - **Magnitude \( v_C \):** Input is 4.0 m/s, marked as incorrect. - **Direction \( v_C \):** Negative x, marked as correct. - **Segment D:** - **Magnitude \( v_D \):** Input is 4.0 m/s, marked as incorrect. - **Direction \( v_D \):** Positive x, marked as correct. #### (b) Average Velocity Calculate the athlete's average velocity over a 60-second interval: - **Magnitude:** Input is 4.0 m/s, marked as incorrect. - **Direction:** Positive x, marked as correct. ### Explanation This exercise focuses on analyzing segments of a velocity graph. Errors in magnitude indicate a need for reevaluation of calculations based on the graph details. Understanding zero magnitude in segment B helps interpret periods of rest. The correct direction selections guide comprehension of directional changes throughout the athlete's movement.
The image shows a graph depicting the movement of an object over time, with distance on the y-axis and time on the x-axis. The y-axis is labeled \(x(m)\) representing distance in meters, while the x-axis is labeled \(t(s)\) indicating time in seconds. The graph is structured as follows:

- **Segment A (0 to 15 seconds):** The graph starts at the origin (0, 0), and the object moves in a positive direction from 0 to 60 meters over the first 15 seconds. This indicates a uniform motion with a steady increase in distance.

- **Segment B (15 to 25 seconds):** From 15 to 25 seconds, the graph is flat at 60 meters, reflecting that the object is stationary during this interval as there is no change in distance over time.

- **Segment C (25 to 40 seconds):** Between 25 and 40 seconds, the graph slopes downwards from 60 meters to 40 meters, indicating the object is moving backward or returning toward the starting point.

- **Segment D (40 to 60 seconds):** In the final segment, from 40 to 60 seconds, the graph shows a steep upward trajectory from 40 meters to 100 meters. This suggests the object is moving forward quickly, covering more distance in a shorter time span.

The graph is divided into sections marked by the letters A, B, C, and D for ease of reference, illustrating different phases of motion over the course of 60 seconds.
Transcribed Image Text:The image shows a graph depicting the movement of an object over time, with distance on the y-axis and time on the x-axis. The y-axis is labeled \(x(m)\) representing distance in meters, while the x-axis is labeled \(t(s)\) indicating time in seconds. The graph is structured as follows: - **Segment A (0 to 15 seconds):** The graph starts at the origin (0, 0), and the object moves in a positive direction from 0 to 60 meters over the first 15 seconds. This indicates a uniform motion with a steady increase in distance. - **Segment B (15 to 25 seconds):** From 15 to 25 seconds, the graph is flat at 60 meters, reflecting that the object is stationary during this interval as there is no change in distance over time. - **Segment C (25 to 40 seconds):** Between 25 and 40 seconds, the graph slopes downwards from 60 meters to 40 meters, indicating the object is moving backward or returning toward the starting point. - **Segment D (40 to 60 seconds):** In the final segment, from 40 to 60 seconds, the graph shows a steep upward trajectory from 40 meters to 100 meters. This suggests the object is moving forward quickly, covering more distance in a shorter time span. The graph is divided into sections marked by the letters A, B, C, and D for ease of reference, illustrating different phases of motion over the course of 60 seconds.
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