Q: Check whether the relation $\large S = u t + \frac{1}{2}a t^2 $ is dimensionally correct or not, where symbols have their usual meaning.
Sol. We have $\large S = u t + \frac{1}{2}a t^2 $ .
checking the dimensions On both sides
$ LHS = [S] = [M^0 L^1 T^0 ] $
$ RHS = [ut] + [\frac{1}{2}a t^2]$
$ =[LT^{-1}][T]+[LT^{-2}][T^2 ]$
$ =[M^0 L^1 T^0 ]+[M^0 L^1 T^0 ]$
$ =[M^0 L^1 T^0 ]$
We find LHS = RHS
Hence, the formula is dimensionally correct.