The principle of dimensional homogeneity states that an equation is dimensionally correct if the dimensions of all the terms on both sides of the equation are the same. In the given equation:

1. The dimension of $x$ (displacement) is $[L]$.
2. The dimension of $vt$ (velocity $[LT^{-1}]$ multiplied by time $[T]$) is $[LT^{-1}][T] = [L]$.
3. The dimension of $\frac{1}{2}at^2$ (a dimensionless constant $\frac{1}{2}$ multiplied by acceleration $[LT^{-2}]$ and time squared $[T^2]$) is $[LT^{-2}][T^2] = [L]$. For the equation to be dimensionally correct, all terms must have the same dimensions, which in this case is $[L]$.