$A$ body of mass $1 \text{ kg}$ moves along a straight line with a velocity $v = 2x^2$. The work done by the body during displacement from $x = 0$ to $5 \text{ m}$ is . . . . . . $J$.

$A$ 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 .........

$A$ particle of mass $500 \,g$ is moving in a straight line with velocity $v = b x^{5/2}$. The work done by the net force during its displacement from $x = 0$ to $x = 4 \,m$ is ................... $J$ (Take $b = 0.25 \,m^{-3/2} s^{-1}$)

$A$ spring of force constant $k$ is fixed vertically on a table. $A$ ball of mass $m$ is dropped from a height $h$ onto the free end of the spring,causing the spring to compress by a distance $d$. What is the total work done in this process?

$A$ pendulum bob on a $2\, m$ string is displaced $60^\circ$ from the vertical and then released. What is the speed of the bob as it passes through the lowest point in its path? (Take $g = 9.8\, m/s^2$)

$A$ bullet of mass $m$ enters a wooden block of length $L$ at a speed $v_1$ and emerges out of the block with a speed $v_2$. If $F$ is the average force which impeded its motion through the wooden block, then (Assume uniform deceleration inside the block):