$A$ particle of mass $500 \text{ g}$ is at rest. It is free to move along a straight line. The power delivered to the particle varies with time according to the following graph. The momentum of the particle at $t = 5 \text{ s}$ is

$A$ particle is acted upon by a force $F$ which varies with position $x$ as shown in the figure. If the particle at $x = 0$ has a kinetic energy of $25\,J$,then the kinetic energy of the particle at $x = 16\,m$ is .............. $J$.

$A$ bullet enters a piece of wood with velocity $v_0$ and the resistive force acting on the bullet in the wood is proportional to $v^{\frac{1}{3}}$. If the total distance travelled by the bullet is proportional to $(v_0)^\beta$,then the value of $\beta$ 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 $20 \; m$.

$A$ force $(3x^2 + 2x - 5) \text{ N}$ displaces a body from $x = 2 \text{ m}$ to $x = 4 \text{ m}$. The work done by this force is .......... $J$.

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 $\text{ J}$)