rearanging
V^2 = Vo^2 + 2 a (X - Xo)
for V gives me
V = (Vo^2 + 2 a (X - Xo))^(2^-1)
or this
V = (Vo + 2 a (X - Xo))^(2^-1)
How come Vo^2 dosen't become Vo
It is rather unusual to write 2^-1 for 1/2, but either is OK.
Vo^2 is not V^2 because the equation says that it isn't. The reasons are due to physics. Velocity decreases when there is deceleration.
Vo^2 can never become V. They have different dimensions. One is squared and the other isn't.
I didn't right Vo^2 as V...
This is what you wrote:
<<How come Vo^2 dosen't become Vo >>
I agree and as you can see I wrote "...Vo^2 dosen't become Vo"
not
""...Vo^2 dosen't become V"
V^2 = Vo^2 + 2 a (X - Xo)
V= sqrt ( Vo^2 + 2 a (X - Xo)
Your algebra is totally wrong.
The initial speed squared Vo^2 is in meters^2/seconds^2
The final speed V is in meters/second
They can never, ever be the same as drwls said.