$A$ toy car of mass $5 \, kg$ moves up a ramp under the influence of a force $F$ plotted against displacement $x$ as shown in the graph. The maximum height attained is given by:

$A$ block of mass $m=1 \; kg$ moving on a horizontal surface with speed $v_{i}=2 \; m \; s^{-1}$ enters a rough patch ranging from $x=0.10 \; m$ to $x=2.01 \; m$. The retarding force $F$ on the block in this range is inversely proportional to $x$ over this range,$F_{r} = -k/x$ for $0.1 < x < 2.01 \; m$,and $F_{r} = 0$ for $x < 0.1 \; m$ and $x > 2.01 \; m$,where $k=0.5 \; J$. What is the final kinetic energy $K_{f}$ and speed $v_{f}$ of the block as it crosses this patch?

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

The components of a force acting on a particle vary according to the graphs shown. To reach point $B\, (8, 20, 0)$ from point $A\, (0, 5, 12)$,the particle moves on paths parallel to the $x$-axis,then the $y$-axis,and then the $z$-axis. The work done by this force is ............ $J$.

If a force of $(6x^2 - 4x) \ N$ acts on a body of mass $10 \ kg$,then the work done by the force in displacing the body from $x = 2 \ m$ to $x = 4 \ m$ is: (in $J$)

$A$ 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............$J$.