The figure shows the relationship between force and position. What is the work done by the force for the displacement of the object from $x = 1 \; cm$ to $x = 5 \; cm$ in ergs?

$A$ 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: ............... $k$

$A$ 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

$A$ woman pushes a trunk on a railway platform which has a rough surface. She applies a force of $100 \; N$ over a distance of $10 \; m$. Thereafter,she gets progressively tired and her applied force reduces linearly with distance to $50 \; N$. The total distance through which the trunk has been moved is $20 \; m$. Plot the force applied by the woman and the frictional force,which is $50 \; N$ versus displacement. Calculate the work done by the two forces over $20 \; m$.

The relationship between the force $F$ and position $x$ of a body is as shown in the figure. The work done in displacing the body from $x = 1 \text{ m}$ to $x = 5 \text{ m}$ will be ........ $J$.

The work done by a force $\vec{F} = -5x^4 \hat{i} \text{ N}$ in displacing a body from $x = 2 \text{ m}$ to $x = -2 \text{ m}$ is: (in $\text{ J}$)