$A$ force acts on a $3.0 \ g$ particle in such a way that the position of the particle as a function of time is given by:
$x = 3t - 4t^2 + t^3$
Where $x$ is in metres and $t$ is in seconds. The work done during the first $4 \ s$ is ................. $mJ$

$A$ 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............$J$.

The graph between the resistive force $F$ acting on a body and the distance $x$ covered by the body is shown in the figure. The mass of the body is $25\, kg$ and the initial velocity is $2\, m/s$. When the distance covered by the body is $4\, m$,its kinetic energy would be .............. $J$.

The slope of the kinetic energy-displacement curve of a particle in motion is

The work done in displacing a particle from $y=a$ to $y=2a$ by a force $F = -\frac{K}{y^2}$ acting along the $y$-axis is:

The kinetic energy $K$ of a particle moving along the $x$-axis varies with its position $x$ as shown in the figure. The magnitude of the force acting on the particle at $x = 9 \ m$ is $.... \ N$.