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The acceleration-time graph of a particle that starts from rest and moving on a straight line is shown in the given figure. Match the quantities of column I with the values in column II and select the correct option from the given?
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The acceleration-time graph of a particle that starts from rest and mo...
Understanding the Acceleration-Time Graph
The acceleration-time graph provides crucial information about the motion of a particle. By analyzing the graph, we can derive several key quantities relevant to the particle's motion.
Key Quantities Derived from the Graph
- Velocity: Since the particle starts from rest, the initial velocity is zero. The area under the acceleration-time graph gives the change in velocity. If the acceleration is positive for a specific duration, the velocity increases.
- Displacement: The displacement can be calculated by finding the area under the velocity-time graph, which is the integral of the velocity over time. After calculating the velocity using the areas of the acceleration graph, we can derive the displacement.
- Time: The total time of motion can be determined from the duration over which the acceleration is applied. This is simply the time interval shown on the x-axis of the graph.
Matching Quantities in Column I and Column II
1. Initial Velocity:
- Value: 0 m/s (since the particle starts from rest)
2. Final Velocity:
- Calculate by integrating the area under the acceleration graph.
3. Displacement:
- Calculate by finding the area under the velocity-time graph derived from acceleration.
4. Total Time:
- The total duration for which acceleration is applied.
Conclusion
By analyzing the acceleration-time graph and calculating the areas, you can derive the required quantities of velocity, displacement, and time. This method of matching the derived quantities to their respective values in a structured manner allows for a clear understanding of the particle's motion.
The acceleration-time graph provides crucial information about the motion of a particle. By analyzing the graph, we can derive several key quantities relevant to the particle's motion.
Key Quantities Derived from the Graph
- Velocity: Since the particle starts from rest, the initial velocity is zero. The area under the acceleration-time graph gives the change in velocity. If the acceleration is positive for a specific duration, the velocity increases.
- Displacement: The displacement can be calculated by finding the area under the velocity-time graph, which is the integral of the velocity over time. After calculating the velocity using the areas of the acceleration graph, we can derive the displacement.
- Time: The total time of motion can be determined from the duration over which the acceleration is applied. This is simply the time interval shown on the x-axis of the graph.
Matching Quantities in Column I and Column II
1. Initial Velocity:
- Value: 0 m/s (since the particle starts from rest)
2. Final Velocity:
- Calculate by integrating the area under the acceleration graph.
3. Displacement:
- Calculate by finding the area under the velocity-time graph derived from acceleration.
4. Total Time:
- The total duration for which acceleration is applied.
Conclusion
By analyzing the acceleration-time graph and calculating the areas, you can derive the required quantities of velocity, displacement, and time. This method of matching the derived quantities to their respective values in a structured manner allows for a clear understanding of the particle's motion.
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The acceleration-time graph of a particle that starts from rest and moving on a straight line is shown in the given figure. Match the quantities of column I with the values in column II and select the correct option from the given?
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The acceleration-time graph of a particle that starts from rest and moving on a straight line is shown in the given figure. Match the quantities of column I with the values in column II and select the correct option from the given? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The acceleration-time graph of a particle that starts from rest and moving on a straight line is shown in the given figure. Match the quantities of column I with the values in column II and select the correct option from the given? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The acceleration-time graph of a particle that starts from rest and moving on a straight line is shown in the given figure. Match the quantities of column I with the values in column II and select the correct option from the given?.
The acceleration-time graph of a particle that starts from rest and moving on a straight line is shown in the given figure. Match the quantities of column I with the values in column II and select the correct option from the given? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The acceleration-time graph of a particle that starts from rest and moving on a straight line is shown in the given figure. Match the quantities of column I with the values in column II and select the correct option from the given? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The acceleration-time graph of a particle that starts from rest and moving on a straight line is shown in the given figure. Match the quantities of column I with the values in column II and select the correct option from the given?.
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