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A particle travels half distance with a velocity of 6 m/s .The remaining half distance is covered with a velocity of 4m/s for half the time with a velocity of 8m/s for the rest of half time.What is the velocity of the particle averaged over the whole time of motion?
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A particle travels half distance with a velocity of 6 m/s .The remaini...
Solution:
Given,
Distance travelled = 2d
Velocity for the first half of distance = 6 m/s
Velocity for the second half of distance = 4 m/s for half the time and 8 m/s for the rest of the half time
We have to find the average velocity of the particle over the entire time of motion.
Calculating the time taken to cover the distance:
Let's assume that the distance travelled is d.
The particle covers the first half distance with a velocity of 6 m/s.
Time taken to cover the first half of distance = d/2v = d/2×6 = d/12
Let's divide the second half distance into two parts.
The particle covers the first half of the second half distance (i.e., d/4) with a velocity of 4 m/s.
Time taken to cover the first half of the second half distance = d/4v = d/4×4 = d/16
The particle covers the rest of the second half distance (i.e., d/4) with a velocity of 8 m/s.
Time taken to cover the rest of the second half distance = d/4v = d/4×8 = d/32
Total time taken = (d/12) + (d/16) + (d/32) = (4d + 3d + d)/96 = 8d/96 = d/12
Calculating the average velocity:
Average velocity of the particle over the entire time of motion = Total distance travelled / Total time taken
Total distance travelled = 2d
Total time taken = d/12
Average velocity of the particle over the entire time of motion = (2d) / (d/12) = 24 m/s
Therefore, the average velocity of the particle over the entire time of motion is 24 m/s.
Given,
Distance travelled = 2d
Velocity for the first half of distance = 6 m/s
Velocity for the second half of distance = 4 m/s for half the time and 8 m/s for the rest of the half time
We have to find the average velocity of the particle over the entire time of motion.
Calculating the time taken to cover the distance:
Let's assume that the distance travelled is d.
The particle covers the first half distance with a velocity of 6 m/s.
Time taken to cover the first half of distance = d/2v = d/2×6 = d/12
Let's divide the second half distance into two parts.
The particle covers the first half of the second half distance (i.e., d/4) with a velocity of 4 m/s.
Time taken to cover the first half of the second half distance = d/4v = d/4×4 = d/16
The particle covers the rest of the second half distance (i.e., d/4) with a velocity of 8 m/s.
Time taken to cover the rest of the second half distance = d/4v = d/4×8 = d/32
Total time taken = (d/12) + (d/16) + (d/32) = (4d + 3d + d)/96 = 8d/96 = d/12
Calculating the average velocity:
Average velocity of the particle over the entire time of motion = Total distance travelled / Total time taken
Total distance travelled = 2d
Total time taken = d/12
Average velocity of the particle over the entire time of motion = (2d) / (d/12) = 24 m/s
Therefore, the average velocity of the particle over the entire time of motion is 24 m/s.
Community Answer
A particle travels half distance with a velocity of 6 m/s .The remaini...
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A particle travels half distance with a velocity of 6 m/s .The remaining half distance is covered with a velocity of 4m/s for half the time with a velocity of 8m/s for the rest of half time.What is the velocity of the particle averaged over the whole time of motion?
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