$A$ particle is acted upon by a force whose components' variations with time are shown in the diagrams. The magnitude of the change in momentum of the particle in $0.1\,s$ is:

$A$ body of mass $5 \, kg$ is moving with a momentum of $10 \, kg \cdot m/s$. $A$ force of $0.2 \, N$ acts on it in the direction of motion of the body for $10 \, seconds$. The increase in its kinetic energy is ............... $J$.

$A$ force is applied to a body of mass $2 \,kg$ at rest on a frictionless horizontal surface, as shown in the force-time $(F-t)$ graph. The speed of the body after $1 \,s$ is: (in $\,m/s$)

$A$ ball of mass $0.5 \ kg$ moving horizontally at $10 \ m \ s^{-1}$ strikes a vertical wall and rebounds with speed $v$. The magnitude of the change in linear momentum is found to be $8.0 \ kg \ m \ s^{-1}$. The magnitude of $v$ is, (in $m \ s^{-1}$)

State whether the following statements are true or false:
$(a)$ The product of the mass of an object and its velocity is called linear momentum.
$(b)$ Inertia is mass,and the measure of inertia is the resistance to change.
$(c)$ Force is the change in momentum.

$A$ machine gun fires $20$ bullets per second into a target. Each bullet weighs $150 \, g$ and has a speed of $800 \, m/s$. Find the force necessary to hold the gun in position.