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A particle moves in a straight line a to b for the first one 4th distance with v0, the next half of distance with speed 2v 0 ,and the last one fourth half distance with speed 3v0 find the average speed?
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A particle moves in a straight line a to b for the first one 4th dista...
Approach:
To find the average speed of the particle, we need to first calculate the total time taken for the particle to move from point A to point B. Then, we can find the total distance traveled by the particle and use the formula for average speed.
Calculations:
- Let the total distance between points A and B be d units.
- The particle first covers 1/4th of the distance, i.e., d/4 units, at a speed of v0.
- The time taken to cover this distance is d/4v0.
- Next, the particle covers half of the remaining distance, i.e., d/2 units, at a speed of 2v0.
- The time taken to cover this distance is d/4v0.
- Finally, the particle covers the last 1/4th distance, i.e., d/4 units, at a speed of 3v0.
- The time taken to cover this distance is d/12v0.
Total Time:
Total time taken = d/4v0 + d/2(2v0) + d/12(3v0)
Total time taken = d/4v0 + d/v0 + d/4v0
Total time taken = 3d/4v0
Total Distance:
Total distance = d/4 + d/2 + d/4
Total distance = d
Average Speed:
Average speed = Total distance / Total time taken
Average speed = d / (3d/4v0)
Average speed = 4v0/3
Therefore, the average speed of the particle moving from point A to point B is 4v0/3.
To find the average speed of the particle, we need to first calculate the total time taken for the particle to move from point A to point B. Then, we can find the total distance traveled by the particle and use the formula for average speed.
Calculations:
- Let the total distance between points A and B be d units.
- The particle first covers 1/4th of the distance, i.e., d/4 units, at a speed of v0.
- The time taken to cover this distance is d/4v0.
- Next, the particle covers half of the remaining distance, i.e., d/2 units, at a speed of 2v0.
- The time taken to cover this distance is d/4v0.
- Finally, the particle covers the last 1/4th distance, i.e., d/4 units, at a speed of 3v0.
- The time taken to cover this distance is d/12v0.
Total Time:
Total time taken = d/4v0 + d/2(2v0) + d/12(3v0)
Total time taken = d/4v0 + d/v0 + d/4v0
Total time taken = 3d/4v0
Total Distance:
Total distance = d/4 + d/2 + d/4
Total distance = d
Average Speed:
Average speed = Total distance / Total time taken
Average speed = d / (3d/4v0)
Average speed = 4v0/3
Therefore, the average speed of the particle moving from point A to point B is 4v0/3.
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A particle moves in a straight line a to b for the first one 4th distance with v0, the next half of distance with speed 2v 0 ,and the last one fourth half distance with speed 3v0 find the average speed?
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A particle moves in a straight line a to b for the first one 4th distance with v0, the next half of distance with speed 2v 0 ,and the last one fourth half distance with speed 3v0 find the average speed? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A particle moves in a straight line a to b for the first one 4th distance with v0, the next half of distance with speed 2v 0 ,and the last one fourth half distance with speed 3v0 find the average speed? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle moves in a straight line a to b for the first one 4th distance with v0, the next half of distance with speed 2v 0 ,and the last one fourth half distance with speed 3v0 find the average speed?.
A particle moves in a straight line a to b for the first one 4th distance with v0, the next half of distance with speed 2v 0 ,and the last one fourth half distance with speed 3v0 find the average speed? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A particle moves in a straight line a to b for the first one 4th distance with v0, the next half of distance with speed 2v 0 ,and the last one fourth half distance with speed 3v0 find the average speed? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle moves in a straight line a to b for the first one 4th distance with v0, the next half of distance with speed 2v 0 ,and the last one fourth half distance with speed 3v0 find the average speed?.
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