Check the correctness of the formula `S = ut + 1/3 "at"^2` where S is the distance , u is velocity , a is acceleration and t is time.

Explanation

Dimensionally, LHS =[L]
RHS = `[LT^-1][T] + [LT^(-2)] [T]^2 = [L]+[L] `
Since , the dimension of each term on both sides are same, the equation is correct dimensionally , However we cannot say anything about the physical correctness of the formula. In fact , we know that the correct formula is S = `ut+ 1/2 "at"^2`
Hence, we conclude that dimensional correctness is no guarantee for physical correctness of the formula. However , dimensional incorrectness guarantees the physical incorrectness of the formula. Inspite to the above limitation, the method is still helpful to a great extent.