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 $Joule$?

In the figure given below,the position-time graph of a particle of mass $0.1 \,kg$ is shown. The impulse at $t = 2 \,s$ is .......... $kg \,m \,s^{-1}$.

$A$ 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:

$A$ block of mass $2\, kg$ is suspended by a string of length $5\, m$. It is released from a horizontal position (as shown in the figure) such that the string is initially slack. What will be the impulse when the string just becomes tight? (Take $g = 10\, m/s^2$)

$N$ bullets,each of mass $m \, kg$,are fired with a velocity $v \, m/s$ at the rate of $n$ bullets per second upon a wall. The reaction force offered by the wall to the bullets is given by:

$A$ small mass $m$ is launched from the top of a cliff with speed $V$ at an angle of $30^{\circ}$ above the horizontal. When the mass reaches the ground,its velocity is directed at $45^{\circ}$ below the horizontal. Which one of the following choices is the magnitude of the total impulse that was imparted to the mass during its flight? Ignore air resistance.