$A$ body of mass $1 \ kg$ is under a force, which causes a displacement given by $x = \frac{t^3}{3}$ (in $m$). Find the work done by the force in the first second (in $J$).

$A$ block of mass $m$ is sliding down an inclined plane with constant speed. At a certain instant $t_0$,its height above the ground is $h$. The coefficient of kinetic friction between the block and the plane is $\mu$. If the block reaches the ground at a later instant $t_g$,then the energy dissipated by friction in the time interval $(t_g - t_0)$ is

$A$ particle is released from a height $s$. At a certain height,its kinetic energy is three times its potential energy. The height and speed of the particle at that instant are respectively:

An open knife edge of mass $50 \ g$ is dropped from a height $2 \ m$ on a wooden floor. If the blade penetrates up to a depth of $10 \ cm$ into the wood,the average resistance offered by the wood to the knife edge is $....N$

$A$ body of mass $0.5\, kg$ travels on a straight-line path with velocity $v = (3x^2 + 4)\, m/s$. The net work done by the force during its displacement from $x = 0$ to $x = 2\, m$ is $.......J$.

$A$ simple pendulum is released from point $A$ as shown in the figure. If $m$ and $l$ represent the mass of the bob and the length of the pendulum respectively,the gain in kinetic energy at point $B$ is: