When is an object said to be in motion? What is meant by the description of an object's motion?

In which of the following examples of motion can the body be considered approximately a point object:
$(a)$ $A$ railway carriage moving without jerks between two stations.
$(b)$ $A$ monkey sitting on top of a man cycling smoothly on a circular track.
$(c)$ $A$ spinning cricket ball that turns sharply on hitting the ground.
$(d)$ $A$ tumbling beaker that has slipped off the edge of a table.

$A$ balloon is moving up in air vertically above a point $A$ on the ground. When it is at a height $h_{1}$,a girl standing at a distance $d$ (point $B$) from $A$ sees it at an angle $45^{\circ}$ with respect to the vertical. When the balloon climbs up a further height $h_{2}$,it is seen at an angle $60^{\circ}$ with respect to the vertical if the girl moves further by a distance $2.464d$ (point $C$). Then the height $h_{2}$ is (given $\tan 30^{\circ} = 0.5774$):

The position of a body moving along the $x$-axis at time $t$ is given by $x = (t^2 - 4t + 6) \, m$. The distance travelled by the body in the time interval $t = 0$ to $t = 3 \, s$ is ...... $m$.

Are motion and position relative or not?

$A$ person travels $10\, km$ north and $20\, km$ east. What will be the displacement from the initial point in $km$?