Check the dimensional correctness for the given equation.
(a) `v=u+at`
(b) `s=ut+1/2at^2`

Explanation

a. `v=u+at` Apply dimensional formual on both sides
`[LT^(-1)]=[LT^(-1)]+[LT^(-2)][T]`
`[LT^(-1)]=[LT^(-1)]+[LT^(-1)]`
(Quantities of same dimension only can be added )
Sicne dimensions on both sides are same, the given equation is dimensionally correct.
b.`[L]=[LT^(-1)][T]+[LT^(-2)][T^(2)]`
`[L]=[LT^(-1+1)]+[LT^(-2+2)]`
`[L]=[LT^(0)]+[LT^(0)]`
`:.[L]=[L]+[L]`
Since dimensions on both sides are same the given equation is dimensionally correct.