To test the validity of a physical equation, we perform unit-wise analysis. In the above physical relation:

$$\rm v^2 = ut$$

In terms of fundamental physical units,

$$\rm (ms^{-2})^2 \neq ms^{-1} \cdot s$$

The fundamental physical units involved in the equation's left-hand sides are not equal to those in the right-hand side of the equation. So, we can conclude that the given relation $\rm v^2 = ut$ is invalid.