Force is the mutual interaction between the bodies according to:

The force $F$ acting on a particle of mass $m$ is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from $0 \, s$ to $8 \, s$ is .......... $N-s$.

$A$ 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:

$A$ player kicks a football of mass $0.5 \ kg$ and the football begins to move with a velocity of $10 \ m/s$. If the contact between the leg and the football lasts for $\frac{1}{50} \ s$,then the force acted on the football should be .......... $N$.

Three different projectiles,each with the same mass $m$,are fired with speed $v$ at a wall. In case $A$,the projectile bounces straight back with speed $v$. In case $B$,the projectile sticks to the wall. In case $C$,the projectile crashes through the wall and emerges with half its original speed. These three cases are shown in the figure. Place the magnitude of the impulse exerted by the wall on the projectile in each of these three cases in the correct order.

In two different experiments,an object of mass $5 \; kg$ moving with a speed of $25 \; ms^{-1}$ hits two different walls and comes to rest within
$(i)$ $3 \; s$,$(ii)$ $5 \; s$,respectively.
Choose the correct option out of the following: