Check the correctness of the equations,
(i) ` s = ut + 1//2 at ^ 2 ` and (ii) ` s _ (nth) = u + (a)/(2) ( 2 n - 1 ) `

Explanation

(1) ` s = ut + 1//2 at ^ 2 `
`[L] = [LT^( -1) ][T]+ [LT^( -2) ][T^( 2 ) ]" " [L] = [L]+[L] `
Since every term on the RHS has the same dimensional formula , the equation is dimensionally correct.
(2) ` s_n th = u + (a)/(2) ( 2n - 1 ) `
` [ (s)/(t)] = [u] + [a][ 2 n - 1]" "i.e., [LT^( -1) ] = [LT^( -1) ] +[LT^( -2) ][T] `
or ` [LT^( -1) ] =[LT^( -1) ] + [LT^( -1) ] `
Since every term on the RHS has the same dimensional formula the equation is dimensionally correct.