The magnitude of force acting on a particle moving along the $x$-axis varies with time $(t)$ as shown in the figure. If at $t=0$ the velocity of the particle is $v_0$,then its velocity at $t=T_0$ will be

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

$A$ man is at rest in the middle of a pond on perfectly smooth ice. He can get himself to the shore by making use of Newton's

If a force of $250\, N$ acts on a body,the momentum acquired is $125\, kg \cdot m/s$. What is the period for which the force acts on the body? ......... $s$

$A$ spherical body of mass $100 \,g$ is dropped from a height of $10 \,m$ from the ground. After hitting the ground, the body rebounds to a height of $5 \,m$. The impulse of force imparted by the ground to the body is given by: (given $g = 9.8 \,m/s^2$)

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