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?

Explanation

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^(20 = 2a (s)/(2)`
From (1) , we get
`v_(0)^(2) - u^(2) = (v^(2) - u^(2))/(2)`
`v_(0)^(2) = (v^(2) - u^(2))/(2) + u^(2)`
`v_(0)^(2) = (v^(2) - u^(2) + 2u^(2))/(2)`
` v_(0) = sqrt((v^(2) + u^(2))/(2))`