The quantities remaining constant in a general collision are

$A$ ball is thrown from $10 \, m$ height at speed $v_0$ vertically downward. Upon colliding with the surface of the earth,it loses $50 \%$ of its energy and again reaches the same height. The value of $v_0$ is: ................. $m/s$

$A$ $70\, kg$ man leaps vertically into the air from a crouching position. To take the leap,the man pushes the ground with a constant force $F$ to raise himself. The center of gravity rises by $0.5\, m$ before he leaves the ground. After the leap,the center of gravity rises by another $1\, m$. The maximum power delivered by the muscles is: (Take $g = 10\, ms^{-2}$)

$A$ simple pendulum of length $1 \,m$ has a wooden bob of mass $M = 1 \,kg$. It is struck by a bullet of mass $m = 10^{-2} \,kg$ moving with a speed of $u = 2 \times 10^2 \,m/s$. The bullet gets embedded into the bob. The height to which the bob rises before swinging back is (use $g = 10 \,m/s^2$): (in $\,m$)

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

Is it possible for the kinetic energy of an object not to increase when work is done on it? If so,when?