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

$A$ force-time graph for a linear motion is shown in the figure,where the segments are circular. The linear momentum gained between $0$ and $8$ seconds is

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).

Action and reaction forces act on

$A$ force of $50 \text{ dynes}$ acts on a body of mass $5 \text{ g}$ which is at rest for an interval of $3 \text{ seconds}$. The impulse is:

$A$ 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 $m \ s^{-1}$)