$A$ particle moves under the effect of a force $F = cx$ from $x = 0$ to $x = x_1$. The work done in the process is

$A$ 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:

Arrange the four graphs in descending order of total work done; where $W_{1}, W_{2}, W_{3}$ and $W_{4}$ are the work done corresponding to Figure-$a$,Figure-$b$,Figure-$c$ and Figure-$d$ respectively.

$A$ force $F = \alpha + \beta x^2$ acts on an object in the $x$-direction. The work done by the force is $5 \ J$ when the object is displaced by $1 \ m$. If the constant $\alpha = 1 \ N$,then $\beta$ will be: (in $N/m^2$)

$A$ 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 force $\vec F = F\hat i$ on a particle of mass $2\, kg$,moving along the $x$-axis is given in the figure as a function of its position $x$. The particle is moving with a velocity of $5\, m/s$ along the $x$-axis at $x = 0$. What is the kinetic energy of the particle at $x = 8\, m$?