The displacement $x$ of a particle moving in one dimension under the action of a constant force is related to time $t$ by the equation $t=\sqrt{x}+3,$ where $x$ is in meters and $t$ is in seconds. What is the displacement of the particle from $t=0~\text s$ to $t = 6~\text s?$

1. $0$
2. $12~\text m$
3. $6~\text m$
4. $18~\text m$

Given below are two statements: 

If the velocity of a particle is $\mathrm{v}=\mathrm{At}+{\mathrm{Bt}}^2$, where A and B are constants, then the distance travelled by it between 1s and 2s is?

$1.$ $3\mathrm{A}+7\mathrm{B}$
$2.$ $\frac{3\mathrm{A}}{2}+\frac{7\mathrm{B}}{3}$
$3.$ $\frac{\mathrm{A}}{2}+\frac{\mathrm{B}}{3}$
$4.$ $\frac{\mathrm{A}}{3}+\frac{\mathrm{B}}{2}$