What is path length? What is displacement?

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(N/A) Path length is the total distance covered by an object during its motion between two points. It is a scalar quantity,meaning it has magnitude but no direction.
Displacement is the change in the position of an object in a particular interval of time. It is defined as the difference between the final position $(x_2)$ and the initial position $(x_1)$: $\Delta x = x_2 - x_1$. Displacement is a vector quantity,as it has both magnitude and direction.
Example: Consider a car moving from origin $O$ $(x=0)$ to point $P$ $(x=360 \ m)$ and then back to point $Q$ $(x=240 \ m)$.
$1$. Path length: The total distance covered is $OP + PQ = 360 \ m + (360 \ m - 240 \ m) = 360 \ m + 120 \ m = 480 \ m$.
$2$. Displacement: The displacement is the final position minus the initial position: $\Delta x = x_Q - x_O = 240 \ m - 0 \ m = +240 \ m$. The positive sign indicates the direction is along the positive $x$-axis.

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Does the displacement of an object depend on the choice of the origin of the coordinate system?

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.
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Give some examples of motion.

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