$A$ bullet is fired at a target with velocity $V$. Its velocity decreases from $V$ to $V/2$ when it penetrates $30 \ cm$ into the target. Through what additional thickness will it penetrate further into the target before coming to rest (in $cm$)?

$A$ body is projected vertically upwards with a velocity of $20 \,m \,s^{-1}$. If the potential energy of the body at a height of $5 \,m$ from the ground is $100 \,J$, then the kinetic energy of the body at a height of $10 \,m$ from the ground is (Acceleration due to gravity $= 10 \,m \,s^{-2}$) (in $\,J$)

$A$ car driver is trying to jump across a path as shown in the figure by driving horizontally off a cliff '$X$' at a speed of $10 \ m \ s^{-1}$. When he touches peak '$Z$' (ignore air resistance), what would be his speed (in $m \ s^{-1}$)? (use $g = 10 \ m \ s^{-2}$)

$A$ bullet of mass $20\,g$ has an initial speed of $1\,ms^{-1}$ just before it starts penetrating a mud wall of thickness $20\,cm.$ If the wall offers a mean resistance of $2.5 \times 10^{-2}\,N,$ the speed of the bullet after emerging from the other side of the wall is close to .............. $ms^{-1}$

What does the law of conservation of energy state?

$A$ car moving with a velocity of $10 \, m/s$ can be stopped by the application of a constant force $F$ in a distance of $20 \, m$. If the velocity of the car is $30 \, m/s$,it can be stopped by this same force in what distance (in $, m$)?