Is second equation of motion valid for non uniform acceleration?

Answer 1

Yes. It just has to be remembered that the equation is describing a balance between

a force and the increment of momentum of the system per time unit on which the force is being applied "at a given instant t".

For a given system with constant mass m, we can write Newton's 2nd law of motion

as:

F(t) = m∙a(t)

where force F(t) and acceleration a(t) are a function of time (notice that if the force

is constant during time applied, acceleration results constant or uniform).

If you know how the force is varying in time (function F(t)), then you know the

function of acceleration in time: a(t) = F(t)/m

Answer 2

Yes, the second equation of motion (v^2 = u^2 + 2as) is valid for non-uniform acceleration as long as the initial and final velocities, acceleration, and displacement are known. This equation relates the final velocity of an object with its initial velocity, acceleration, and displacement.