$A$ particle of mass $500 \text{ g}$ is at rest. It is free to move along a straight line. The power delivered to the particle varies with time according to the following graph. The momentum of the particle at $t = 5 \text{ s}$ is

$A$ body of $0.5 \,kg$ moves along the positive $X$-axis under the influence of a varying force $F$ (in newton) as shown below. If the speed of the object at $x=4 \,m$ is $3.16 \,ms^{-1}$,then its speed at $x=8 \,m$ is ................. $\,ms^{-1}$.

$A$ bullet of mass $1 \ kg$ fired with a speed $2 \ m \ s^{-1}$ from $x = 0$ passes through a block of wood whose centre is kept at a distance of $10 \ m$ from the origin as shown in figure. The retarding force $F_r$ on the bullet within the wooden block is $-0.5/x$. The minimum length of the block (up to $1$ decimal digit) required to completely stop the bullet is (Assume $e^4 = 55$). (in $m$)

In a one-dimensional case,the relationship between force and position is shown in the figure. The work done by the force in displacing a body from $x = 1\, cm$ to $x = 5\, cm$ is ............ $ergs$.

The work done by a force acting on a body is as shown in the graph. The total work done in covering an initial distance of $20 \, m$ is (in $ \, J$)

$A$ body of mass $3 \ kg$ moves under the influence of a force such that its displacement is given by $s = t^3/3 \ m$. What is the work done by the force in the first $2 \ s$ in $J$?