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.