Lets use Dimensional analysis.
[tex]\\ \sf\longmapsto s=ut+\dfrac{1}{2}at^2[/tex]
[tex]\\ \sf\longmapsto s=\left[M^0LT^0\right][/tex]
[tex]\\ \sf\longmapsto ut+\dfrac{1}{2}at^2[/tex]
[tex]\\ \sf\longmapsto \left[M^0LT^{-1}\right]\left[M^0L^0T^1\right]+\dfrac{1}{2}\left[M^0LT^{-2}\right]\left[M^0L^0T^1\right]^2[/tex]
[tex]\\ \sf\longmapsto L+\dfrac{1}{2}\left[LT^{-2}\right]\left[T^2\right][/tex]
[tex]\\ \sf\longmapsto L+\dfrac{1}{2}L[/tex]
[tex]\\ \sf\longmapsto \dfrac{2L}{2}[/tex]
[tex]\\ \sf\longmapsto [L^1][/tex]
[tex]\\ \sf\longmapsto \left[M^0LT^0\right][/tex]
LHS=RHS
Hence verified
