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A particle traversed on third of the dis...

A particle traversed on third of the distance with a velocity `v_(0)`, the remaining part of the distance was covered with velocity `v_(1)` for half the time and with a velocity `v_(2)` for the remaining half of time. Assuming motion to be rectilinear, find the the mean velocity of the particle averaged over the whole time of motion.

Text Solution

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for AC, `(S)/(3) = v_(0)t_(1) rArr t_(1) = (S)/(3v_(0)) ….. (1)`
For CB, `(2S)/(3) = CD + DB`
`rArr (2S)/(3) = v_(1)((t_(2))/(2)) + v_(2)((t_(2))/(2)) rArr t_(2) = (4S)/(3(v_(1) + v_(2)))`
Since, average velocity is defined as
`v_(avg) = ("Total Displacement")/("Total Time") = ((S)/(3)+(2S)/(3))/(t_(1) + (t_(2))/(2) + (t_(2))/(2)) = (S)/(t_(1) + t_(2))`
`rArr v_(avg) = (3v_(0)(v_(1) + v_(2)))/(4v_(0) + v_(1) + v_(2))`
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