Can the kinetic energy of an object be negative? Can the potential energy be negative?

$A$ rubber ball is dropped from a height of $5 \ m$ on a planet,where the acceleration due to gravity is not known. On bouncing,it rises to $1.8 \ m$. The ball loses its velocity on bouncing by a factor of

$A$ particle of mass $m = 2 \ kg$ is initially at rest. The force $(F)$ versus displacement $(x)$ graph is shown in the figure.
$(1)$ The speed of the particle will be maximum at $x = ..... \ m$.
$(2)$ The maximum speed of the particle is ...... $ms^{-1}$.
$(3)$ The speed of the particle will be zero again at $x = .... \ m$.

$A$ ball of mass $m$ falls vertically to the ground from a height $h_1$ and rebounds to a height $h_2$. The change in momentum of the ball on striking the ground is

Two bodies $A$ and $B$ of mass $m$ and $2m$ respectively are placed on a smooth floor. They are connected by a spring of negligible mass. $A$ third body $C$ of mass $m$ is placed on the floor. The body $C$ moves with a velocity $v_0$ along the line joining $A$ and $B$ and collides elastically with $A$. At a certain time after the collision,it is found that the instantaneous velocities of $A$ and $B$ are the same and the compression of the spring is $x_0$. The spring constant $k$ will be

$A$ bullet moving with a velocity of $100\, m/s$ can just penetrate two planks of equal thickness. The number of such planks penetrated by the same bullet,when the velocity is doubled,will be