The position-time graph of a body of mass $2\, kg$ is as given in the figure. What is the impulse on the body at $t = 0\, s$ and $t = 4\, s$ (in $, Ns$)?

Two billiard balls of equal mass $30 \, g$ strike a rigid wall with the same speed of $108 \, km/h$ (as shown) but at different angles. If the balls get reflected with the same speed, then the ratio of the magnitude of impulses imparted to ball $'a'$ and ball $'b'$ by the wall along the $'X'$ direction is:

Using the variation of force and time given below, the final velocity of a particle of mass $2 \, kg$ moving with an initial velocity $6 \, m/s$ will be: (in $m/s$)

$A$ mass of $1 \ kg$ is suspended by a string $A$. Another string $C$ is connected to its lower end as shown in figure. If a sudden jerk is given to $C$,then

$A$ machine gun fires a bullet of mass $40\,g$ with a velocity $1200\,m/s$. The man holding it can exert a maximum force of $144\,N$ on the gun. How many bullets can he fire per second at the most?

$A$ body of $2\, kg$ has an initial speed of $5\, ms^{-1}$. $A$ force acts on it for some time in the direction of motion. The force-time graph is shown in the figure. Find the final speed of the body in $ms^{-1}$.