Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time \(t_1.\) On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time \(t_2.\) The time taken by her to walk upon the moving escalator will be:

Two cars P and Q start from a point at the same time in a straight line and their positions are represented by $x_p\left(t\right)=at+b{t}^2$ and $x_Q\left(t\right)=ft-t^2$. At what time do the cars have the same velocity?

(1) $\frac{a-f}{1+b}$

(2)$\frac{a+f}{2\left(b-1\right)}$

(3) $\frac{a+f}{2\left(1+b\right)}$

(4) $\frac{f-a}{2\left(1+b\right)}$

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?

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

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