A particle of mass $m$ is constrained to move on $x$-axis. A force $F$ acts on the particle. $F$ always points toward the position labeled E. For example, when the particle is to the left of $E$, $F$ points to the right. The magnitude of $F$ is constant except at point $E$ where it is zero.
The system is horizontal. $F$ is the net force acting on the particle. The particle is displaced a distance A towards left from the equilibrium position $E$ and released from rest at $t=0$
Velocity-time graph of the particle is

A body of mass $m_1$ exerts a force on another body of mass $m_2$. If the magnitude of acceleration of $m_2$ is $a_2$, then the magnitude of the acceleration of $m_1$ is (considering only two bodies in space)

A large number $(n)$ of identical beads, each of mass $m$ and radius $r$ are strung on a thin smooth rigid horizontal rod of length $L\, (L >> r)$ and are at rest at random positions. The rod is mounted between two rigid supports (see figure) . If one of the beads is now given a speed $v$, the average force experienced by each support after a long time is (assume all collisions are elastic)

Define impulse of force. Time derivative of momentum gives which physical quantity ?

A man is pulling on a rope attached to a block on a smooth horizontal table. The tension in the rope will be the same at all points

Give the magnitude and direction of the net force acting on a stone of mass $0.1\; kg$,

$(a)$ just after it is dropped from the window of a stationary train,

$(b)$ just after it is dropped from the window of a train running at a constant velocity of $36 \;km/h$,

$(c)$ just after it is dropped from the window of a train accelerating with $1\; m s^{-2}$,

$(d)$ lying on the floor of a train which is accelerating with $1\; m s^{-2}$, the stone being at rest relative to the train.

Neglect air resistance throughout.