$A$ particle of mass $1\, kg$ is acted upon by a force $F$ which varies as shown in the figure. If the initial velocity of the particle is $10\, ms^{-1}$, the maximum velocity attained by the particle during the period is ........ $ms^{-1}$.

$A$ 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:

$A$ 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:

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:

$A$ machine gun can fire $200$ bullets $\min^{-1}$. If $35 \ g$ bullets are fired at a speed of $750 \ m \ s^{-1}$, the average force exerted by the gun on the bullets is, (in $N$)

$A$ player caught a cricket ball of mass $150 \ g$ moving at a speed of $20 \ m/s$. If the catching process is completed in $0.1 \ s$,the magnitude of the force exerted by the ball on the hand of the player is .......... $N$.