What is the relationship between the displacement and the path length of a moving object?

Three girls skating on a circular ice ground of radius $200 \; m$ start from a point $P$ on the edge of the ground and reach a point $Q$ diametrically opposite to $P$ following different paths as shown in the figure. What is the magnitude of the displacement vector for each? For which girl is this equal to the actual length of the path skated?

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 ...... $m$.

$A$ boy walks uniformly along the sides of a rectangular park of size $400 \, m \times 300 \, m$,starting from one corner to the diagonally opposite corner. Which of the following statements is incorrect?

When are the path length and the magnitude of displacement the same?

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.