$A$ 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 .......... $N$.

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

$A$ body of mass $m$ collides against a wall with a velocity $v$ and rebounds with the same speed. Its change of momentum is

$A$ particle moves in the $x-y$ plane under the action of a force $\overrightarrow{F}$ such that the value of its linear momentum $\overrightarrow{P}$ at any time $t$ is $P_x = 2\cos t$ and $P_y = 2\sin t$. The angle $\theta$ between $\overrightarrow{F}$ and $\overrightarrow{P}$ at a given time $t$ will be $\theta = $ ........... $^o$.

$A$ gun applies a force $F$ on a bullet which is given by $F = (100 - 0.5 \times 10^{5} t) \ N$. The bullet emerges out with a speed of $400 \ m/s$. Find the impulse exerted until the force on the bullet becomes zero (in $N \cdot s$).

An object of mass $5 \ kg$ is moving with a momentum of $10 \ kg \cdot m/s$. If a force of $0.2 \ N$ is applied on it in the direction of its motion for $10 \ s$,what is the increase in its kinetic energy in $Joule$?