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A particle moving with uniform accelerat...

A particle moving with uniform acceleration from `A` to `B` along a straight line has velcities `v_(1)` and `v_(2)` at `A` and `B` respectively. If `C` is the mid-point between `A` and `B` then determine the velocity of the particle at `C` .
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Text Solution

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Let `v` be the velocity of the particle at `c`. Assume the acceleration of the particle to be `A` and distance between `A` and `B` be `x`. To find the velocity `c`, consider the motion from `A`and `C`:
Applying `v^(2)-u^(2)=2` as, we get `v^(2)-v_(1)^(2)=2a(x)/(2)`
`rArr v^(2)-v_(1)^(2)=ax`........ (i)
Appying the same equation from `C` to `B`. we get`
`V_(2)^(2)=2a(x)/(2) rArr v_(2)^(2)-v^(2)=ax` ......(ii)
From (i) and (ii), we get `v=sqrt(v_(1)^(2)+v_(2)^(2))/(2)`.
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