$A$ body of $2\, kg$ has an initial speed of $5\, ms^{-1}$. $A$ force acts on it for some time in the direction of motion. The force-time graph is shown in the figure. Find the final speed of the body in $ms^{-1}$.

$A$ force-time graph for a linear motion is shown in the figure,where the segments are circular. The linear momentum gained between $0$ and $8$ seconds is

$A$ 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 $g = 10\, m/s^2$)

$A$ 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 = $ ........... $^o$.

$A$ batsman deflects a ball by an angle of $45^{\circ}$ without changing its initial speed,which is equal to $54 \; km/h$. What is the impulse imparted to the ball in $kg \; m/s$? (Mass of the ball is $0.15 \; kg$.)

$A$ force acting on a body varies with time as shown below. If the initial momentum of the body is $\vec{p}$,then the time taken by the body to regain its momentum $\vec{p}$ again is ........... $s$.