$A$ body of mass $2 \, kg$ is thrown vertically upwards with a velocity of $4 \, m/s$. At what height will its kinetic energy be half of its initial value (in $, m$)? (Take $g = 10 \, m/s^2$)

The velocity-time graph for a body of mass $10 \ kg$ is shown in the figure. The work done on the body in the first two seconds of motion is:

$A$ bullet fired from a gun into a large wooden block loses half of its velocity after traveling $6 \ cm$ inside the block. How much further distance (in $cm$) will it travel before coming to rest?

The velocity-time graph for a body of mass $10\, kg$ is shown in the figure. The work done on the body in the first two seconds of the motion is ................ $J$.

State the principle of conservation of mechanical energy for a conservative force.

$A$ spherical ball of mass $20 \, kg$ is stationary at the top of a hill of height $100 \, m$. It slides down a smooth surface to the ground,then climbs up another hill of height $30 \, m$ and finally slides down to a horizontal base at a height of $20 \, m$ above the ground. The velocity attained by the ball is ............... $m/s$.