Power applied to a particle varies with time as $P = (3t^2 - 2t + 1) \text{ W}$. The change in kinetic energy of the particle from $t = 2 \text{ s}$ to $t = 4 \text{ s}$ is ............... $J$.

$A$ position-dependent force $F$ acts on a particle,and its force-position curve is shown in the figure. The work done on the particle for a displacement from $0$ to $5\,m$ 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 $\overrightarrow F = - K(y\hat i + x\hat j)$ (where $K$ is a positive constant) acts on a particle moving in the $x-y$ plane. Starting from the origin,the particle is taken along the positive $x$-axis to the point $(a, 0)$ and then parallel to the $y$-axis to the point $(a, a)$. The total work done by the force $\overrightarrow F$ on the particle is

$A$ $10 \, kg$ mass moves along the $x-$axis. Its acceleration as a function of its position is shown in the figure. What is the total work done on the mass by the force as the mass moves from $x = 0$ to $x = 8 \, cm$?

$A$ graph of potential energy $V(x)$ versus $x$ is shown in the figure. $A$ particle of energy $E_0$ is executing motion in it. Draw the graph of velocity and kinetic energy versus $x$ for one complete cycle $AFA$.