The time in which a force of $2 \,N$ produces a change of momentum of $0.4\,kg – m{s^{ – 1}}$ in the body is ……… $\sec$

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

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 $v ( t )= v _0^{ e ^{-1 / \tau}}$, where $v_0$ is a constant and $\tau=4 s$. The displacement of the block, in metres, at $t=\tau$ is. . . . . . . Take $e ^{-1}=0.37$

A women throws an object of mass $500\,g$ with a speed of $25\, ms^{-1}$.

$(a)$ What is the impulse imparted to the object ?

$(b)$ If the object hits a wall and rebounds with half the original speed, what is the change in momentum of the object ?