$A$ bullet of mass $10 \ g$ is fired with a velocity of $800 \ m/s$. After passing through a mud wall of thickness $1 \ m$,its velocity decreases to $100 \ m/s$. Find the average resistive force exerted by the mud wall in $N$.

$A$ particle of mass $m \ kg$ moves along the $X$-axis with its velocity varying with the distance travelled as $v=k x^\beta$,where $k$ is a positive constant. The total work done by all the forces during displacement of the particle from $x=0$ to $x=d$ is close to

$A$ body of mass $6 \,kg$ is acted upon by a force which causes a displacement in it given by $x = \frac{t^2}{4} \,m$,where $t$ is the time in seconds. The work done by the force in $2 \,seconds$ is: (in $\,J$)

$A$ body of mass $m$ is moving with uniform acceleration such that at time $t_1$ its velocity is $v$. What is the work done on the body at any time $t$?

Under the action of a force,a $2 \, kg$ body moves such that its position $x$ as a function of time $t$ is given by $x = \frac{t^2}{3}$,where $x$ is in metres and $t$ is in seconds. The work done by the force in the first two seconds is .......... $J$.

$A$ bullet of mass $10 \; g$ leaves a rifle at an initial velocity of $1000 \; m/s$ and strikes the earth at the same level with a velocity of $500 \; m/s$. The work done in joule $(J)$ in overcoming the resistance of air will be: