Check the correctness of the following equation using dimensional analysis. Make a comment on it. `S= u t+ 1//4 a t^(2)` where s is the displacement, u is the initial velocity, t is the time and a is the acceleration produced.

Explanation

By the principle of homogeneity, `a//V^(2)` is of the dimensions of pressure  and b is of the dimensions of volume.
[a] = [pressure] `[V^(2)]= [ML^(-1) T^(-2)] [L^(6)]= [ML^(5)T^(-2)]`
[b] `=[V]= L^(3)`