$A$ block of mass $2 \ kg$ moves freely along the $x$-axis. It is at rest at $t = 0$. The force $F(t)$ acting on the block varies with time $t$ as shown in the figure. What is the kinetic energy of the block after $4.5 \ s$ (in $J$)?

$A$ 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:

$A$ mass of $1 \ kg$ is suspended by a string $A$. Another string $C$ is connected to its lower end as shown in figure. If a sudden jerk is given to $C$,then

$A$ $40 \ g$ ball dropped from a certain height bounces back from the horizontal ground without losing mechanical energy. If its speed is $10 \ m/s$ just before making contact with the ground,and the average value of the force of the ground on the ball is $16 \ N$ while the ball and ground are in contact,how long were they in contact in milliseconds $(ms)$?

$A$ ball of mass $0.5 \ kg$ is dropped from a height of $40 \ m$. The ball hits the ground and rises to a height of $10 \ m$. The impulse imparted to the ball during its collision with the ground is (Take $g = 9.8 \ m/s^2$)

What is impulse of force? Write its unit and dimension.