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

$A$ particle of mass $10\,g$ moves in a straight line with retardation $2x$,where $x$ is the displacement in $SI$ units. Its loss of kinetic energy for the above displacement is $\left(\frac{10}{x}\right)^{-n}\,J$. The value of $n$ will be $............$.

$A$ $10 \, kg$ 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 $x = 8 \, cm$?

Power delivered to a mass is $P = (3t^2 - 2t + 1) \text{ W}$. The change in kinetic energy from $t = 2 \text{ s}$ to $t = 4 \text{ s}$ is: .................... $J$

The force-displacement graph for a particle is given. Calculate the work done by the force as the particle moves from $x = 1 \ cm$ to $x = 5 \ cm$. (in $erg$)

$A$ bar of mass $m$ resting on a smooth horizontal plane starts moving due to force $|\vec{F}|=\frac{mg}{9}$. The magnitude of the force remains constant with time. The force vector makes an angle $\theta$ with the horizontal which varies with the distance covered as $\theta= Cx$. If the constant $C=10 \text{ degree/meter}$, then the speed of the bar, when $\theta$ becomes equal to $30^{\circ}$ for the first time, is (Assume $g = 10 \text{ m s}^{-2}$) (in $\text{ m s}^{-1}$)