$A$ particle is acted upon by a force $F$ which varies with position $x$ as shown in the figure. If the particle at $x = 0$ has a kinetic energy of $25\,J$,then the kinetic energy of the particle at $x = 16\,m$ is .............. $J$.

The force $F$ acting on a particle moving in a straight line varies with distance $d$ as shown in the figure. The work done on the particle during its displacement of $12\, m$ is ................. $J$.

The displacement $s$ of a body of mass $3 \,kg$ under the action of a force is given by $s = \frac{t^3}{3}$,where $s$ is in metres and $t$ is in seconds. The work done by the force in the first two seconds is (in $\,J$)

$A$ particle moves under the effect of a force $F = cx$ from $x = 0$ to $x = x_1$. The work done in the process is

The kinetic energy $(E_k)$ of a particle moving along the $X$-axis varies with its position $(X)$ as shown in the figure. The force acting on the particle at $X = 10 \ m$ is

$A$ bullet enters a piece of wood with velocity $v_0$ and the resistive force acting on the bullet in the wood is proportional to $v^{\frac{1}{3}}$. If the total distance travelled by the bullet is proportional to $(v_0)^\beta$,then the value of $\beta$ is