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A body travelling along a straight line traversed one-third of the total distance with a velocity v1. The remaining part of the distance was covered with a velocity v2 for half the time and with velocity v3 for the other half of time. The mean velocity averaged over the whole time of motion?
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A body travelling along a straight line traversed one-third of the tot...
Problem statement: A body travelling along a straight line traversed one-third of the total distance with a velocity v1. The remaining part of the distance was covered with a velocity v2 for half the time and with velocity v3 for the other half of time. Find the mean velocity averaged over the whole time of motion.
Solution:
To find the mean velocity averaged over the whole time of motion, we need to use the formula:
Mean velocity = (Total distance travelled) / (Total time taken)
Let us first find the distances travelled at different velocities:
Distance travelled with velocity v1 = (1/3) x Total distance
Distance travelled with velocity v2 = (1/2) x (2/3) x Total distance = (1/3) x Total distance
Distance travelled with velocity v3 = (1/2) x (2/3) x Total distance = (1/3) x Total distance
Total distance travelled = (1/3) x Total distance + (1/3) x Total distance + (1/3) x Total distance = Total distance
Now, let us find the time taken at different velocities:
Time taken with velocity v1 = (1/3) x Total distance / v1
Time taken with velocity v2 = (1/2) x (2/3) x Total distance / v2 = (1/3) x Total distance / v2
Time taken with velocity v3 = (1/2) x (2/3) x Total distance / v3 = (1/3) x Total distance / v3
Total time taken = (1/3) x Total distance / v1 + (1/3) x Total distance / v2 + (1/3) x Total distance / v3
Therefore, the mean velocity averaged over the whole time of motion is:
Mean velocity = Total distance / [(1/3) x Total distance / v1 + (1/3) x Total distance / v2 + (1/3) x Total distance / v3]
Mean velocity = 3 / [(1/v1) + (1/v2) + (1/v3)]
Therefore, the mean velocity averaged over the whole time of motion is given by the harmonic mean of the three velocities v1, v2, and v3.
Answer:
The mean velocity averaged over the whole time of motion is given by the harmonic mean of the three velocities v1, v2, and v3. Therefore, the answer is:
Mean velocity = 3 / [(1/v1) + (1/v2) + (1/v3)]
Solution:
To find the mean velocity averaged over the whole time of motion, we need to use the formula:
Mean velocity = (Total distance travelled) / (Total time taken)
Let us first find the distances travelled at different velocities:
Distance travelled with velocity v1 = (1/3) x Total distance
Distance travelled with velocity v2 = (1/2) x (2/3) x Total distance = (1/3) x Total distance
Distance travelled with velocity v3 = (1/2) x (2/3) x Total distance = (1/3) x Total distance
Total distance travelled = (1/3) x Total distance + (1/3) x Total distance + (1/3) x Total distance = Total distance
Now, let us find the time taken at different velocities:
Time taken with velocity v1 = (1/3) x Total distance / v1
Time taken with velocity v2 = (1/2) x (2/3) x Total distance / v2 = (1/3) x Total distance / v2
Time taken with velocity v3 = (1/2) x (2/3) x Total distance / v3 = (1/3) x Total distance / v3
Total time taken = (1/3) x Total distance / v1 + (1/3) x Total distance / v2 + (1/3) x Total distance / v3
Therefore, the mean velocity averaged over the whole time of motion is:
Mean velocity = Total distance / [(1/3) x Total distance / v1 + (1/3) x Total distance / v2 + (1/3) x Total distance / v3]
Mean velocity = 3 / [(1/v1) + (1/v2) + (1/v3)]
Therefore, the mean velocity averaged over the whole time of motion is given by the harmonic mean of the three velocities v1, v2, and v3.
Answer:
The mean velocity averaged over the whole time of motion is given by the harmonic mean of the three velocities v1, v2, and v3. Therefore, the answer is:
Mean velocity = 3 / [(1/v1) + (1/v2) + (1/v3)]
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A body travelling along a straight line traversed one-third of the tot...
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A body travelling along a straight line traversed one-third of the total distance with a velocity v1. The remaining part of the distance was covered with a velocity v2 for half the time and with velocity v3 for the other half of time. The mean velocity averaged over the whole time of motion?
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