Which of the following options correctly describes the variation of the speed $v$ and acceleration $a$ of a point mass falling vertically in a viscous medium that applies a force $F = -kv$,where $k$ is a constant,on the body? (Graphs are schematic and not drawn to scale)

The curve between net force and time is shown. Initially,the particle is at rest. Which of the following best represents the resulting velocity-time graph of the particle?

Given $m_1 = 4m_2$. How much extra distance (in $cm$) does $m_2$ travel before coming to rest?

$A$ constant force $F$ is applied in the horizontal direction as shown. If the contact force between $M$ and $m$ is $N$ and the contact force between $m$ and $M'$ is $N'$,then:

In the figures $(i), (ii)$ and $(iii)$ shown, the objects $A, B$ and $C$ have the same mass $m$. The string, spring, and pulley are massless. Object $C$ strikes object $B$ with velocity $u$ in each case and sticks to it. Find the ratio of the velocity of $B$ in case $(i)$ to $(ii)$ to $(iii)$.

$A$ parachutist with a total mass of $75 \,kg$ drops vertically onto sandy ground with a speed of $2 \,m/s$ and comes to a halt over a distance of $0.25 \,m$. The average force exerted by the ground on her is close to ............ $N$.