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

$A$ body of mass $0.5 \ kg$ is supplied with a power $P$ (in watt) which varies with time $t$ (in second) as $P = 3t^2 + 3$. If the velocity of the body at time $t = 0$ is zero,then the velocity of the body at time $t = 3 \ s$ is (in $ms^{-1}$)

$A$ box of mass $3 \,kg$ moves on a horizontal frictionless table and collides with another box of mass $3 \,kg$ initially at rest on the edge of the table at height $1 \,m$. The speed of the moving box just before the collision is $4 \,m/s$. The two boxes stick together and fall from the table. The kinetic energy just before the boxes strike the floor is (Assume, acceleration due to gravity, $g=10 \,m/s^2$) (in $\,J$)

$A$ body of mass $4 \,kg$ is moving with momentum of $8 \,kg \,m/s$. $A$ force of $0.2 \,N$ acts on it in the direction of motion of the body for $10 \,s$. The increase in kinetic energy in joules is

Consider two blocks $A$ and $B$ of masses $m_1 = 10 \ kg$ and $m_2 = 5 \ kg$ that are placed on a frictionless table. The block $A$ moves with a constant speed $v = 3 \ m/s$ towards the block $B$ kept at rest. $A$ spring with spring constant $k = 3000 \ N/m$ is attached to the block $B$ as shown in the figure. After the collision,suppose that the blocks $A$ and $B$,along with the spring in a constant compression state,move together. Then the compression in the spring is (neglect the mass of the spring). (in $m$)

This question has Statement-$1$ and Statement-$2$. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement-$1$: $A$ point particle of mass $m$ moving with speed $u$ collides with a stationary point particle of mass $M$. If the maximum energy loss possible is given as $f \left( \frac{1}{2} m u^2 \right)$, then $f = \left( \frac{m}{M + m} \right)$.
Statement-$2$: Maximum energy loss occurs when the particles get stuck together as a result of the collision.