The potential energy $U(x)$ of a system is represented in the figure. The force $F(x)$ acting on the system will be represented by:

$A$ force acts on a body of mass $10 \ kg$, resulting in its displacement given as $x = \left(\frac{t^3}{25}\right) \ m$, where $t$ is the time in seconds. The work done by the force in the first $2 \ s$ is (in $J$)

$A$ body moves from $x = 0$ to $x = x_1$ under the influence of a force $F = cx$. The work done during this process 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 $.... \ N$.

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 $t = 4 \, s$. ............... $J$

The area of the acceleration-displacement curve of a body gives