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What is the speed of the body moving wit...

What is the speed of the body moving with uniform acceleration at the midpoint of two points on a straight line, where the speeds are u and v respectively ?

Text Solution

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Let "a" be the constant acceleration. And s be the distance between the two points.
From equation of motion `v^(2)-u^(2)=2as" "....(1)`
Let `v_(0)` be the speed of the body at midpoint 'M' of the given points.
Applying the same equation used above, we get
`v_(0)^(2)-u^(2)=(2as)/2`
From (1), `v_(0)^(2)-u^(2)=(v^(2)-u^(2))/2`
After some algebra we get, `v_(0)=sqrt((v^(2)+u^(2))/2)`
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