Force of $1000 \mathrm{N}$ acts on a particle parallel to its direction of motion which is horizontal. Its velocity increases from $1 \mathrm{m} {\mathrm{s}}^{–1} \mathrm{to} 10 \mathrm{m} {\mathrm{s}}^{–1},$ when the force acts through a distance of $4 \mathrm{m}$. Calculate the mass of the particle. Given that a force of $10 \mathrm{N}$ is necessary for overcoming friction.

A body of mass $2 \mathrm{kg}$ initially at rest moves under the action of an applied horizontal force of $7 \mathrm{N}$ on a table with the coefficient of kinetic friction $=0.1$. Compute the

(a) work done by the applied force in $10 \mathrm{s}$.

(b) work done by the friction in $10 \mathrm{s}$.

(c) work done by the net force on the body in $10 \mathrm{s}$.

(d) change in kinetic energy of the body in $10 \mathrm{s}$, and interpret your results.

A body of mass $5 \mathrm{kg}$ is acted upon by a variable force. The force varies with the distance covered by the body. What is the speed of the body when the body has covered $25 \mathrm{m}$? Assume that the body starts from rest.

Consider the situation shown in the figure. Initially the spring is undeformed when the system is released from rest. Assuming no friction in the pulley, find the maximum elongation of the spring. 

A rigid body of mass $0.3 \mathrm{kg}$ is taken slowly up an inclined plane of length $10 \mathrm{m}$ and height $5 \mathrm{m}$ (assuming the applied force to be parallel to the inclined plane), and then allowed to slide down to the bottom again. The coefficient of friction between the body and the plane is $0.15.$ Using $g=9.8 \mathrm{m} {\mathrm{s}}^{-2}$  find the 

(a) work done by the gravitational force over the round trip.
(b) work done by the applied force over the upward journey
(c) work done by frictional force over the round trip.
(d) kinetic energy of the body at the end of the trip?

As shown in the figure, there is pulley-block system. The system is released from rest and the block of mass $2 \mathrm{kg}$ is found to have a speed $0.3 \mathrm{m} {\mathrm{s}}^{-1}$ after it has descended through a distance of $2 \mathrm{m}$. Find the coefficient of kinetic friction between the block and the table. $(g=10 \mathrm{m} {\mathrm{s}}^{-2})$