Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time t₁. On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time t₂. The time taken by her to walk upon the moving escalator will be:

1. $\frac{t_1{t}_2}{t_2-t_1}$

2. $\frac{t_1{t}_2}{t_2+t_1}$

3. $t_1-t_2$

4. $\frac{t_1+t_2}{2}$

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 \(\mathrm{v}=\mathrm{At}+\mathrm{Bt^{2}},\) where \(\mathrm{A}\) and \(\mathrm{B}\) are constants, then the distance travelled by it between \(1\) s and \(2\) s is:

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

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

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

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