The position-time $(x-t)$ graph of a moving body of mass $2 \, kg$ is shown in the figure. The impulse on the body at $t=4 \, s$ is

$A$ rigid ball of mass $m$ strikes a rigid wall at $60^\circ$ and gets reflected without loss of speed as shown in the figure. The value of impulse imparted by the wall on the ball will be

$A$ particle moves in the $x-y$ plane under the influence of a force $\vec{F}$ such that its linear momentum is $\vec{P}(t) = \hat{i} \cos(kt) - \hat{j} \sin(kt)$. If $k$ is a constant,the angle between $\vec{F}$ and $\vec{P}$ will be:

$A$ force-time $(F-t)$ graph for a linear motion is shown in the following figure. The segments shown are circular. The linear momentum gained between $0$ and $8 \,s$ is

$A$ body of mass $5 \,kg$ is moving with a velocity of $\vec{v}=(2 \hat{i}+6 \hat{j}) \,m/s$ at $t=0 \,s$. After time $t=2 \,s$,the velocity of the body is $(10 \hat{i}+6 \hat{j}) \,m/s$. The change in momentum of the body is ......... $kg \cdot m/s$.

$A$ body of mass $M$ hits normally a rigid wall with velocity $V$ and bounces back with the same velocity. The impulse experienced by the body is