Check the dimensional consistency of the following equations :
(i) `upsilon = u +at` (ii) `s = ut +(1)/(2) at^2`
(iii) `upsilon^2 - u^2 = 2as`

Explanation

`[x] =L`
`[ut]=velocity xxtime =("length")/("time") xx time =L`
`[(1)/(2) at^(2)] = [at^(2)]= "accelecration" xx(time)^(2)`
`( :. (1)/(2) "is a numbers hence dimentionless")`
`=("velocity")/("time")xx("time")^(2) =("length"//"time")/("time" )xx("time)^(2) =L`
Thus , the equation is correct as far as the dimensions are concerned .