$A$ particle starts from origin $O$ from rest and moves with a uniform acceleration along the positive $x$-axis. Identify all figures that correctly represent the motion qualitatively. ($a =$ acceleration,$v =$ velocity,$x =$ displacement,$t =$ time)

Consider a particle moving along the positive direction of the $X$-axis. The velocity of the particle is given by $v = \alpha \sqrt{x}$ (where $\alpha$ is a positive constant). At time $t = 0$,the particle is located at $x = 0$. Find the time dependence of the velocity and the acceleration of the particle,respectively.

If the displacement of a particle varies with time as $\sqrt{x} = t + 7$,then

The velocity of an object is given by $v = kt$,where $k = 2 \, m/s^2$. What distance (in $m$) will it cover in the first $3 \, s$?

If a train travelling at $72 \text{ km/h}$ is to be brought to rest in a distance of $200 \text{ m}$,then its retardation should be ............ $\text{m/s}^2$.

$A$ driver applies the brakes on seeing the red traffic signal $400 \ m$ ahead. At the time of applying brakes,the vehicle was moving with $15 \ m/s$ and retarding at $0.3 \ m/s^2$. The distance of the vehicle from the traffic light one minute after the application of brakes is: (in $m$)