Force acting on a body of mass $1 \ kg$ is related to its position $x$ as $F = x^3 - 3x \ N$. It is at rest at $x = 1$. Its velocity at $x = 3$ can be ......... $m/s$.

$A$ bar of mass $m$ resting on a smooth horizontal plane starts moving due to force $|\vec{F}|=\frac{mg}{9}$. The magnitude of the force remains constant with time. The force vector makes an angle $\theta$ with the horizontal which varies with the distance covered as $\theta= Cx$. If the constant $C=10 \text{ degree/meter}$, then the speed of the bar, when $\theta$ becomes equal to $30^{\circ}$ for the first time, is (Assume $g = 10 \text{ m s}^{-2}$) (in $\text{ m s}^{-1}$)

$A$ 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

$A$ 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 $m$)

The graph of the resistive force acting on an object versus the distance covered by it is shown in the figure. The mass of the object is $2 \ kg$ and its initial velocity is $10 \ m/s$. When the distance covered by the object is $4 \ m$,its kinetic energy will be $.... \ J$. (in $J$)

$A$ body of mass $2.4 \, kg$ is subjected to a force which varies with distance as shown in the figure. The body starts from rest at $x=0$. Its velocity at $x=9 \, m$ is