EHKEN t (3) O 3 04 Which of the graphs of velocity versus time describes the motion of a particle with the largest displacement ? O O O 2 5 (1) 1 (2) (5)

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Chapter1: Units, Trigonometry. And Vectors
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### Velocity-Time Graphs Analysis

The image displays five velocity versus time graphs representing the motion of a particle. Each graph is labeled from (1) to (5) and shows different velocity behaviors over the same time period.

#### Graph Details:

1. **Graph (1):** 
   - The velocity is constant and positive over time, indicated by a horizontal line above the time axis.

2. **Graph (2):** 
   - The velocity is constant and negative over time, depicted by a horizontal line below the time axis.

3. **Graph (3):** 
   - The velocity increases linearly from zero, forming a diagonal line with a positive slope starting from the time axis.

4. **Graph (4):** 
   - The velocity decreases linearly from a positive value, shown by a diagonal line with a negative slope starting from above the time axis and intersecting the time axis.

5. **Graph (5):** 
   - The velocity is initially constant and positive, then decreases to zero, indicated by a horizontal section followed by a diagonal line with a negative slope ending at the time axis.

#### Question:

*Which of the graphs of velocity versus time describes the motion of a particle with the largest displacement?*

Below are the options for selecting the graph that represents the largest displacement:

- ○ 3
- ○ 4
- ○ 2
- ○ 5
- ○ 1

*Note:* Displacement is determined by the area under the velocity-time graph. The graph with the largest positive area contributes to the largest positive displacement.
Transcribed Image Text:### Velocity-Time Graphs Analysis The image displays five velocity versus time graphs representing the motion of a particle. Each graph is labeled from (1) to (5) and shows different velocity behaviors over the same time period. #### Graph Details: 1. **Graph (1):** - The velocity is constant and positive over time, indicated by a horizontal line above the time axis. 2. **Graph (2):** - The velocity is constant and negative over time, depicted by a horizontal line below the time axis. 3. **Graph (3):** - The velocity increases linearly from zero, forming a diagonal line with a positive slope starting from the time axis. 4. **Graph (4):** - The velocity decreases linearly from a positive value, shown by a diagonal line with a negative slope starting from above the time axis and intersecting the time axis. 5. **Graph (5):** - The velocity is initially constant and positive, then decreases to zero, indicated by a horizontal section followed by a diagonal line with a negative slope ending at the time axis. #### Question: *Which of the graphs of velocity versus time describes the motion of a particle with the largest displacement?* Below are the options for selecting the graph that represents the largest displacement: - ○ 3 - ○ 4 - ○ 2 - ○ 5 - ○ 1 *Note:* Displacement is determined by the area under the velocity-time graph. The graph with the largest positive area contributes to the largest positive displacement.
Expert Solution
Introduction

To find the graph which describes the motion of a particle with the largest displacement.

The area of a velocity-time graph gives:

Area=v×t=displacement

Hence, the larger the area, larger is the displacement.

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