Power applied to a particle varies with time as $P = (4t^3 - 5t + 2) \, W$,where $t$ is in seconds. Find the change in its $K.E.$ between time $t = 2 \, s$ and $t = 4 \, s$. ............... $J$

$A$ 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

The force $F$ acting on a body varies with its position $x$ as shown in the figure. At which point is the body in unstable equilibrium?

$A$ person pushes a box on a rough horizontal platform surface. He applies a force of $200\, N$ over a distance of $15\, m$. Thereafter,he gets progressively tired and his applied force reduces linearly with distance to $100\, N$. The total distance through which the box has been moved is $30\, m$. What is the work done by the person during the total movement of the box $........J$?

The adjacent figure shows the force-displacement graph of a moving body. The work done in displacing the body from $x = 0$ to $x = 35\,m$ is equal to ........... $J$.

$A$ 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 ............... $unit$.