$A$ block of mass $2\, kg$ is suspended by a string of length $5\, m$. It is released from a horizontal position (as shown in the figure) such that the string is initially slack. What will be the impulse when the string just becomes tight? (Take $g = 10\, m/s^2$)

In projectile motion,two particles of masses $m_1$ and $m_2$ have velocities $\vec{V}_1$ and $\vec{V}_2$ respectively at time $t=0$. Their velocities become $\vec{V}_1^{\prime}$ and $\vec{V}_2^{\prime}$ at time $2t$ while still moving in air. The value of $[(m_1 \vec{V}_1^{\prime} + m_2 \vec{V}_2^{\prime}) - (m_1 \vec{V}_1 + m_2 \vec{V}_2)]$ is ($g =$ acceleration due to gravity).

$A$ machine gun fires bullets of mass $30 \text{ g}$ with a velocity of $1000 \text{ m/s}$. The man holding the gun can exert a maximum force of $300 \text{ N}$ on it. How many bullets can he fire per second at most?

The figure shows the position-time $(x-t)$ graph of one-dimensional motion of a body of mass $0.4 \; kg$. The magnitude of each impulse is:

The figure shows the position-time graph of a particle of mass $4 \,kg$. What is the
$(a)$ force on the particle for $t < 0$,$t > 4 \,s$,and $0 < t < 4 \,s$?
$(b)$ impulse at $t = 0$ and $t = 4 \,s$? (Consider one-dimensional motion only).

$A$ 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 $\,m/s$)