$\mathrm{x}=\mathrm{At}+\left(\frac{1}{2}\right){\mathrm{Bt}}^2$  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. Therefor, dimensionally, 

$\left[\mathrm{At}\right]=\left[{\mathrm{Bt}}^2\right]$ i.e., ${\mathrm{LT}}^{-1}{\mathrm{T}}^1=\left[\mathrm{B}\right]\left[{\mathrm{T}}^2\right]$ or

$\left[\mathrm{B}\right]=\frac{\mathrm{L}}{{\mathrm{T}}^2}=\left[{\mathrm{LT}}^{-2}\right]=\left[{\mathrm{M}}^0{\mathrm{L}}^1{\mathrm{T}}^{-2}\right]$