The force $F$ acting on a particle of mass $m$ is indicated by the force-time graph shown below. The change in momentum of the particle over the time interval from zero to $8\, s$ is   ………. $N-s$

In two different experiments, an object of mass $5\; kg$ moving with a speed of $25\; ms ^{-1}$ hits two different walls and comes to rest within

$(i)$ $3$ second, $(ii)$ $5$ seconds, respectively.

Choose the correct option out of the following :

A particle of mass m moving with a velocity $u$ makes an elastic one dimensional collision with a stationary particle of mass $m$ establishing a contact with it for extremely small time $T$. Their force of contact increases from zero to $F_0$ linearly in time $\frac{T}{4}$, remains constant for a further time $\frac{T}{2}$ and decreases linearly from  $F_0$  to zero in further time $\frac{T}{4}$ as shown. The magnitude possessed by $F_0$  is

A particle of mass $m$, initially at rest, is acted upon by a variable force $F$ for a brief interval of time $T$. It begins to move with a velocity $u$ after the force stops acting. $F$ is shown in the graph as a function of time. The curve is a semicircle.