Here, dv/dt is rate of change of velocity, v is velocity and t is time.

So, dimension of $A=\left[L T^{-2}\right] /[T]=\left[L T^{-1}\right]$

$\therefore$ dimension of $\mathrm{A}=\left[\mathrm{L} T^{-3}\right]$

Dimension of $\mathrm{B}=\left[\mathrm{L} T^{-2}\right] /\left[\mathrm{L} T^{-1}\right]=\left[\mathrm{T}^{-1}\right]$

$\therefore$ dimension of $\mathrm{B}=\left[\mathrm{T}^{-1}\right]$