Yes, the equation v^2=u^2+2as is dimensionally correct.
The dimensions of the variables in the equation are as follows: - v (final velocity) has dimensions of length/time - u (initial velocity) has dimensions of length/time - a (acceleration) has dimensions of length/time^2 - s (displacement) has dimensions of length
Substituting these dimensions into the equation, we get: (length/time)^2 = (length/time)^2 + 2(length/time^2)(length)
This simplifies to: (length^2/time^2) = (length^2/time^2) + 2(length^2/time^2)