$A$ body of mass $2 \,kg$ moving in $X-Y$ plane has a potential energy given by $U = (6x + 8y) \,J$. The body is at rest at the point $(3, 2) \,m$. The work done by the body to reach another position after $2 \,s$ is: (in $\,J$)

The average force necessary to stop a bullet of mass $20\, g$ moving with a speed of $250\, m/s$,as it penetrates into the wood for a distance of $12\, cm$ is

$A$ particle of mass $2 \,kg$ travels along a straight line with velocity $v = a \sqrt{x}$,where $a$ is a constant. The work done by the net force during the displacement of the particle from $x = 0$ to $x = 4 \,m$ is .........

$A$ pendulum bob has a speed $4 \,m/s$ at its lowest position. The pendulum is $1 \,m$ long. When the length of the string makes an angle of $60^{\circ}$ with the vertical, the speed of the bob at that position is (acceleration due to gravity, $g=10 \,m/s^2, \cos 60^{\circ}=0.5$).

$A$ bus moving on a level road with a velocity $v$ can be stopped at a distance of $x$ by the application of a retarding force $F$. The load on the bus is increased by $25\%$ by boarding the passengers. Now, if the bus is moving with the same speed and if the same retarding force is applied, the distance travelled by the bus before it stops is

$A$ student of mass $M$ is $1.5 \,m$ tall and has her centre of mass $1 \,m$ above the ground when standing straight. She wants to jump up vertically. To do so,she bends her knees so that her centre of mass is lowered by $0.2 \,m$ and then pushes the ground by a constant force $F$. As a result,she jumps up such that the maximum height of her feet is $0.3 \,m$ above the ground. The ratio $F / Mg$ is (in $.5$)