Check the correctness of the relation S = ut + `1/2at^2` using dimensional analysis.

Explanation

`[S]M^(0)LT^(0)`, `[u]=M^(0)LT^(-1)`
`[t]=M^(0)L^(0)T`, `[a]=M^(0)LT^(-2)` and `(1)/(2)` is a dimensionless constant .
Substituting the dimensional formula on the R.H.S in the given relation, we have
`[ut+(1)/(2)at^(2)]=(LT^(-1))(T)+(LT^(-2))(T^(2))=(M^(0)LT^(0))+(M^(0)LT^(0))=M^(0)LT^(0)`.
Also `[S]=M^(0)LT^(0)`. Since , dimensions are same on both sides, so relation is correct.