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A point traversed half the distance with...

A point traversed half 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 velocity `v_(2)` for the other half of the time. Find the mean velocity of the point averaged over the whole time of the motion.

Text Solution

Verified by Experts

The correct Answer is:
(A)-q, (B)-p, q (C)-p, r, (D)-r, s
`[A] X=3t^(2)+2rArr V=(dx)/(dt)=6t rArr a=(d^(2)x)/(dt^(2))`
`[B] V=8trArr a=(dv)/(dt)=8`
[D] For changing the direction `6t-3t^(2)=0`
`rArr t=0, 2` sec
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Knowledge Check

  • A vehicle travels half the distance l with speed v_(1) and the other half with speed v_(2) then its average speed is

    A
    `(v _(1) + v _(2))/( 2)`
    B
    `(2v _(1) + v _(2))/(v _(1) + v_(2))`
    C
    `(2v _(1) +v _(2))/(v _(1) + v _(2))`
    D
    `(L (v _(1) + v _(2)))/(v _(1) v _(2))`

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