$A$ block of mass $2 \ kg$ is initially at rest on a horizontal frictionless surface. $A$ horizontal force $\overrightarrow{F} = (9 - x^2) \hat{i} \ N$ acts on it, starting from $x = 0$. The maximum kinetic energy of the block between $x = 0$ and $x = 3 \ m$ in joules is:

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 ................. $J$.

$A$ particle experiences a variable force $\overrightarrow{F} = (4x \hat{i} + 3y^2 \hat{j})$ in a horizontal $x-y$ plane. Assume distance is in meters and force is in newtons. If the particle moves from point $(1, 2)$ to point $(2, 3)$ in the $x-y$ plane,the kinetic energy changes by............$J$.

$A$ force $(3x^2 + 2x - 5) \text{ N}$ displaces a body from $x = 2 \text{ m}$ to $x = 4 \text{ m}$. The work done by this force 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 of mass $0.1 \, kg$ is subjected to a force which varies with distance as shown in the figure. If it starts its journey from rest at $x = 0$,its velocity at $x = 12 \, m$ is .......... $m/s$.