$x=At+\left(\frac{1}{2}\right)B{t}^2$ is a dimensionally correct equation, where t is time and A is velocity. The dimensions of B are

When two quantities are added (or subtracted) they must have the same dimensions. Therefore, dimensionally

$\left[At\right]=\left[B{t}^2\right]i.e,L{T}^{-1}{T}^{-1}=\left[B\right]\left[T^2\right]$ or $\left[B\right]=\frac{L}{T^2}=\left[L{T}^{-2}\right]=\left[M^0{L}^1{T}^{-2}\right]$