The force $F$ is given by the equation $F = at + bt^2$,where $t$ is time. What are the dimensions of $a$ and $b$?

If momentum $(P)$,area $(A)$,and time $(T)$ are taken to be fundamental quantities,then energy has the dimensional formula of:

If force $(F)$,velocity $(V)$,and time $(T)$ are taken as fundamental units,then the dimensions of mass are:

$A$ gas bubble formed from an explosion under water oscillates with a period $T$,proportional to $P^{a} d^{b} E^{c}$,where $P$ is the static pressure,$d$ is the density of water,and $E$ is the energy of explosion. Then $a, b, c$ are,respectively:

$A$ force is represented by $F = ax^2 + bt^{1/2}$,where $x$ is distance and $t$ is time. The dimensions of $b^2/a$ are:

In the relation $P = \frac{\alpha}{\beta} e^{-\frac{\alpha Z}{k\theta}}$,$P$ is pressure,$Z$ is distance,$k$ is Boltzmann constant,and $\theta$ is temperature. The dimensional formula of $\beta$ is: