The magnitude of force acting on a particle moving along the $x$-axis varies with time $(t)$ as shown in the figure. If at $t=0$ the velocity of the particle is $v_0$,then its velocity at $t=T_0$ will be

$A$ solid horizontal surface is covered with a thin layer of oil. $A$ rectangular block of mass $m = 0.4 \ kg$ is at rest on this surface. An impulse of $1.0 \ N \ s$ is applied to the block at time $t = 0$ so that it starts moving along the $x$-axis with a velocity $v(t) = v_0 e^{-t/\tau}$,where $v_0$ is a constant and $\tau = 4 \ s$. The displacement of the block,in metres,at $t = \tau$ is. . . . . . . Take $e^{-1} = 0.37$.

In the figure given below,the position-time graph of a particle of mass $0.1 \,kg$ is shown. The impulse at $t = 2 \,s$ is .......... $kg \,m \,s^{-1}$.

$A$ force of $10 \, N$ acts on a body of mass $20 \, kg$ for $10 \, s$. The change in its momentum is ........... $kg \cdot m/s$.

What is linear momentum? Represent it in formula form.

$A$ 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.