Displacement of a particle of mass $2\, kg$ moving in a straight line varies with time as $s = (2t^3 + 2)\, m$. The impulse of the force acting on the particle over a time interval between $t = 0$ and $t = 1\, s$ is .......... $N-s$.

When a $4 \,kg$ rifle is fired,the $10 \,g$ bullet receives an acceleration of $3 \times 10^6 \,cm/s^2$. The magnitude of the force acting on the rifle (in newton) is ............

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:

$A$ particle of mass $m$ moving with velocity $(3\hat{i} + 2\hat{j}) \ m/s$ collides with another body of mass $M$ and finally moves with velocity $(-2\hat{i} + \hat{j}) \ m/s$. Then during the collision:

$Assertion$ : $A$ quick collision between two bodies is more violent than a slow collision,even when the initial and final velocities are identical.
$Reason$ : The rate of change of momentum is greater in the first case.

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