Which of the following options correctly describes the variation of the speed $v$ and acceleration $a$ of a point mass falling vertically in a viscous medium that applies a force $F = -kv$,where $k$ is a constant,on the body? (Graphs are schematic and not drawn to scale)

$A$ $100 \ kg$ gun fires a ball of $1 \ kg$ horizontally from a cliff of height $500 \ m$. It falls on the ground at a distance of $400 \ m$ from the bottom of the cliff. The recoil velocity of the gun is (Acceleration due to gravity $= 10 \ ms^{-2}$). (in $ms^{-1}$)

$A$ vehicle without passengers is moving on a frictionless horizontal road with velocity $u$ and can be stopped in a distance $d$. Now,$40\%$ of its weight is added. If the retardation remains the same,what is the stopping distance at velocity $u$?

$A$ block of mass $m$ is on an inclined plane of angle $\theta$. The coefficient of friction between the block and the plane is $\mu$ and $\tan \theta > \mu$. The block is held stationary by applying a force $P$ parallel to the plane. The direction of force pointing up the plane is taken to be positive. As $P$ is varied from $P_1 = mg(\sin \theta - \mu \cos \theta)$ to $P_2 = mg(\sin \theta + \mu \cos \theta)$,the frictional force $f$ versus $P$ graph will look like:

$A$ ball of mass $2 \ kg$ is moving in $xy$-plane with a potential energy given as $U=(12x + 16y) \ J$, where $x$ and $y$ are in metres. Assume the initial position of the ball at $t=0$ is at the origin $(0,0)$ and it is moving with a velocity of $(15 \hat{i} + 20 \hat{j}) \ m/s$. Identify the correct statement.

When a body moves with some friction on a surface,