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

$A$ body of mass $200\,g$ is moving along the $XY$ plane. The work performed by the force given by $\vec F = (2x\hat i + y\hat j)$ acting on it when the body is displaced from $(0, 0)$ to $(1, 2)$ will be equal to ............... $unit$.

$A$ force $\vec F = k(y\hat i + x\hat j)$ where $k$ is a positive constant acts on a particle moving in the $x-y$ plane. The particle moves along a straight line from the point $(3, 5)$ to $(5, 7)$. The work done by the force is: ............... $k$

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

$A$ 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:

When a rubber band is stretched by a distance $x$,it exerts a restoring force of magnitude $F = ax + bx^2$,where $a$ and $b$ are constants. The work done in stretching the unstretched rubber band by $L$ is