The fourth equation of motion is
$S_n=u+\frac{a}{2}(2 n-1)$
Here $S_n$ is the distance travelled in $n^{\text {th }}$ second which is basically the difference of distances travelled in $n^{\text {th }}$ second and $(n-1)^{\text {th }}$ second. Dimension of $S_n$ is $[\mathrm{L}]$ as it is the measure of distance.
This equation seems to be dimensionally incorrect but it is correct. This equation is derived for a time difference of $1 \mathrm{~s}$. It is basically
$s_n=u(1 s)+\frac{a}{2}\left(2 n(1 s)-(1 s)^2\right)$
So, It is dimensionally consistent.
