Velocity O 3 Time, s (1) st Velocity Velocity + Time (4) Time, s (2) Velocity + Velocity + Time, s (5) Five particles undergo motion as shown in the velocity versus time graphs. In which graph of velocity versus time does a particle end up furthest from the origin (starting point)? Time, s (3) 5

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**Title: Analyzing Motion through Velocity-Time Graphs**

**Introduction**
In this section, we explore how the motion of particles is represented using velocity versus time graphs. Five different graphs depict distinct motion patterns over a period of 5 seconds.

**Graph Descriptions:**

1. **Graph (1):** 
   - Initially has a positive velocity.
   - Gradually decreases to zero by 5 seconds.

2. **Graph (2):**
   - Starts at zero velocity.
   - Shows a steady positive increase, reaching a positive velocity at 5 seconds.

3. **Graph (3):**
   - Positive initial velocity.
   - Increases further into a more positive velocity by 5 seconds.

4. **Graph (4):**
   - Begins with a positive velocity.
   - Increases to a higher velocity, then returns to zero and goes negative at 5 seconds.

5. **Graph (5):**
   - Starts with a negative velocity.
   - Moves to zero and continues into positive velocity by 5 seconds.

**Question**
Five particles undergo motion as shown in the velocity versus time graphs. In which graph does a particle end up furthest from the origin (starting point)?

**Options**
- 5
- 3
- 1
- 2
- 4

**Explanation**
To find the graph where the particle ends up furthest from the starting point, consider the area under each curve (the integral of velocity) over the time period. Positive areas indicate distances moving away from the starting point. Calculate or consider the total distance traveled to determine the furthest distance.

**Conclusion**
Understanding velocity-time graphs is essential in predicting the motion and displacement of particles over time. Use this knowledge to analyze different motion scenarios and solve related problems effectively.
Transcribed Image Text:**Title: Analyzing Motion through Velocity-Time Graphs** **Introduction** In this section, we explore how the motion of particles is represented using velocity versus time graphs. Five different graphs depict distinct motion patterns over a period of 5 seconds. **Graph Descriptions:** 1. **Graph (1):** - Initially has a positive velocity. - Gradually decreases to zero by 5 seconds. 2. **Graph (2):** - Starts at zero velocity. - Shows a steady positive increase, reaching a positive velocity at 5 seconds. 3. **Graph (3):** - Positive initial velocity. - Increases further into a more positive velocity by 5 seconds. 4. **Graph (4):** - Begins with a positive velocity. - Increases to a higher velocity, then returns to zero and goes negative at 5 seconds. 5. **Graph (5):** - Starts with a negative velocity. - Moves to zero and continues into positive velocity by 5 seconds. **Question** Five particles undergo motion as shown in the velocity versus time graphs. In which graph does a particle end up furthest from the origin (starting point)? **Options** - 5 - 3 - 1 - 2 - 4 **Explanation** To find the graph where the particle ends up furthest from the starting point, consider the area under each curve (the integral of velocity) over the time period. Positive areas indicate distances moving away from the starting point. Calculate or consider the total distance traveled to determine the furthest distance. **Conclusion** Understanding velocity-time graphs is essential in predicting the motion and displacement of particles over time. Use this knowledge to analyze different motion scenarios and solve related problems effectively.
Expert Solution
Step 1

Given,

The displacement covered by a particle in the velocity-time graph is given by the area under the velocity-time graph so to calculate the total displacement of the particle we need to calculate the total area under the v-t graph. 

In this, the v-t which has only a positive area will only be able to go up to the furthest point.

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