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A person travelling on a straight line moves with a uniform velocity v1 for a distance x and with a uniform velocity v2 for the next equal distance. the average velocity v is given by?
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A person travelling on a straight line moves with a uniform velocity v...
Understanding Average Velocity
When a person travels equal distances at different velocities, calculating the average velocity involves understanding the total distance covered and the total time taken.
Distance Covered
- The total distance covered is the sum of the two equal distances:
- Distance 1: x (at velocity v1)
- Distance 2: x (at velocity v2)
- Total distance = x + x = 2x
Time Taken
- The time taken for each segment can be calculated using the formula: time = distance/velocity.
- Time for Distance 1:
- t1 = x/v1
- Time for Distance 2:
- t2 = x/v2
- Total time = t1 + t2 = x/v1 + x/v2
Calculating Average Velocity
- Average velocity (v) is defined as total distance divided by total time:
v = Total Distance / Total Time
- Plugging in the values:
v = 2x / (x/v1 + x/v2)
- Simplifying this expression:
v = 2 / (1/v1 + 1/v2)
- This can also be expressed as:
v = (2 * v1 * v2) / (v1 + v2)
Conclusion
The average velocity, when traveling equal distances at different speeds, is given by the harmonic mean of the two velocities. This approach highlights the importance of considering both distance and time to understand average velocity accurately.
When a person travels equal distances at different velocities, calculating the average velocity involves understanding the total distance covered and the total time taken.
Distance Covered
- The total distance covered is the sum of the two equal distances:
- Distance 1: x (at velocity v1)
- Distance 2: x (at velocity v2)
- Total distance = x + x = 2x
Time Taken
- The time taken for each segment can be calculated using the formula: time = distance/velocity.
- Time for Distance 1:
- t1 = x/v1
- Time for Distance 2:
- t2 = x/v2
- Total time = t1 + t2 = x/v1 + x/v2
Calculating Average Velocity
- Average velocity (v) is defined as total distance divided by total time:
v = Total Distance / Total Time
- Plugging in the values:
v = 2x / (x/v1 + x/v2)
- Simplifying this expression:
v = 2 / (1/v1 + 1/v2)
- This can also be expressed as:
v = (2 * v1 * v2) / (v1 + v2)
Conclusion
The average velocity, when traveling equal distances at different speeds, is given by the harmonic mean of the two velocities. This approach highlights the importance of considering both distance and time to understand average velocity accurately.
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A person travelling on a straight line moves with a uniform velocity v1 for a distance x and with a uniform velocity v2 for the next equal distance. the average velocity v is given by?
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A person travelling on a straight line moves with a uniform velocity v1 for a distance x and with a uniform velocity v2 for the next equal distance. the average velocity v is given by? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A person travelling on a straight line moves with a uniform velocity v1 for a distance x and with a uniform velocity v2 for the next equal distance. the average velocity v is given by? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A person travelling on a straight line moves with a uniform velocity v1 for a distance x and with a uniform velocity v2 for the next equal distance. the average velocity v is given by?.
A person travelling on a straight line moves with a uniform velocity v1 for a distance x and with a uniform velocity v2 for the next equal distance. the average velocity v is given by? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A person travelling on a straight line moves with a uniform velocity v1 for a distance x and with a uniform velocity v2 for the next equal distance. the average velocity v is given by? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A person travelling on a straight line moves with a uniform velocity v1 for a distance x and with a uniform velocity v2 for the next equal distance. the average velocity v is given by?.
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