Rectilinear Motion - Displacement

• Displacement measures how far and in which direction an object moves.
• It is the change in the object’s position between two times.
• Displacement is a vector quantity, so it has both magnitude and direction.
• Its unit is the metre (m).
• Direction is given by the line along which the object moves.

If the position at time t₁ is x₁ and at time t₂ is x₂, then
Displacement \[\vec s\] = \[\vec x_2\] - \[\vec x_1\]

In vector form:

\[\Delta\bar{r}=(x_2-x_1)\hat{i}+(y_2-y_1)\hat{j}+(z_2-z_1)\hat{k}\]

• Displacement depends only on initial and final positions.
• It does not depend on the path taken between the two points.
• It has the same dimensions as length ([L]).
• It is positive, negative, or zero depending on direction.
• Its direction is along the line of motion.

• Walking 5 m east from home and stopping: displacement = 5 m east.
• Swimming straight 20 m toward the shore: displacement = 20 m toward shore.
• Driving from school to home, 3 km south: displacement = 3 km south.
• A bird flying 10 m up from a tree branch: displacement = 10 m upward.

The shortest straight line distance between an object's initial and final positions, represented as Δ\[\vec x\] = \[\vec x_2\] − \[\vec x_1\]​​, is called displacement.

OR

The shortest distance from the initial to the final position of a body undergoing motion — a vector quantity whose direction is always from initial to final position, which does not depend on path but only on initial and final positions, and may be positive, negative, or zero — is called displacement.

The total length of the actual path covered by a body in travelling from its initial to its final position — a scalar quantity that always depends on the path followed, can never be negative, and has SI unit metre (m) — is called distance.