$A$ body of mass $3\, kg$ is under a force,which causes a displacement given by $S = \frac{t^3}{3}$ (in $m$). Find the work done by the force in the first $2\, s$.

$A$ person pushes a box on a rough horizontal platform surface. He applies a force of $200\, N$ over a distance of $15\, m$. Thereafter,he gets progressively tired and his applied force reduces linearly with distance to $100\, N$. The total distance through which the box has been moved is $30\, m$. What is the work done by the person during the total movement of the box $........J$?

$A$ body of mass $8\,kg$ is moved by a force $F = 3x\,N$,where $x$ is the distance covered. The initial position is $x = 2\,m$ and the final position is $x = 10\,m$. The initial speed is $0.0\,m/s$. The final speed is ........... $m/s$.

The adjacent figure shows the force-displacement graph of a moving body. What is the work done by this force in displacing the body from $x = 0$ to $x = 35\,m$ (in $,J$)?

$A$ 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 $20 \; m$.

$A$ force of $F=(5 y+20) \hat{j} \, N$ acts on a particle. The work done by this force when the particle is moved from $y=0 \, m$ to $y=10 \, m$ is $... \, J.$