Let's say I have a function defined as a module where at the end I call up "Manipulate" as below:
a[x_]:= Module[{k},k = 2 x; Manipulate[Something[y], {y, 0, k}]
What does Mathematica complain about the variablek? It says "a variable was used where it is probably not going to be evaluated before going out of scope"
Is there any way I can fix this and achieve what I want?
Don't use Module in the situation you describe. Module is a lexical scoping construct. The k give to Module as its 1st argument is a statically scoped variable. Your Manipulate expression builds its own dynamically scoping regime, so the k mentioned in your specification of the manipulator control y is in a different scope and is a different variable. Look at your code wrapped in FullForm to see that this is so.
The fix is to use DynamicModule in place of Module.
a[x_] :=
DynamicModule[{k},
k = 2 x;
Manipulate[
1/y^k,
{y, .1, k, Appearance -> "Labeled"}]]
a[.5]
