An athlete runs for some distance before taking a long jump. Why?

Two bodies $A$ and $B$ collide as shown in Fig. $(i)$ and $(ii)$. Which statement is true?

$A$ 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 ........... $s$.

$A$ time-varying force acts on a ball of mass $100 \ g$ for $2 \ ms$. The force versus time curve is shown below. If the initial speed of the ball is $10 \ m \ s^{-1}$,then the speed of the ball after $2 \ ms$ is: (in $m \ s^{-1}$)

$A$ solid horizontal surface is covered with a thin layer of oil. $A$ rectangular block of mass $m = 0.4 \ kg$ is at rest on this surface. An impulse of $1.0 \ N \ s$ is applied to the block at time $t = 0$ so that it starts moving along the $x$-axis with a velocity $v(t) = v_0 e^{-t/\tau}$,where $v_0$ is a constant and $\tau = 4 \ s$. The displacement of the block,in metres,at $t = \tau$ is. . . . . . . Take $e^{-1} = 0.37$.

What is linear momentum? Represent it in formula form.