Position and Reference Point

To describe motion, we choose a reference point (often origin) and a coordinate axis (positive/negative direction). An object’s position is defined relative to this point.

  • Example: If a car is 10 m east of a lamp post (taken as origin), its position is +10 m.

Displacement vs Distance

  • Displacement: Change in position. It is a vector with direction. [\Delta x = x_{\text{final}} - x_{\text{initial}}]
  • Distance: Total path length covered. It is a scalar and always non-negative.

Key Differences

Feature Distance Displacement
Type Scalar Vector
Direction No Yes
Zero or Non-zero Always ≥ 0 Can be 0, +ve, or −ve
Depends on Path Initial & final positions

Example:

A person walks 4 m east and 3 m west:

  • Distance = 4+3=7 m4 + 3 = 7\ \text{m}
  • Displacement = 4−3=1 m4 - 3 = 1\ \text{m} (east)

Displacement depends only on start and end points, not the path.

Example:

A car travels from point A to B to C. AB = 40 m east, BC = 30 m west. Find:

  • Distance travelled
  • Displacement

Solution:

  • Distance = 40+30=70 m40 + 30 = 70\ \text{m}
  • Displacement = 40−30=10 m40 - 30 = 10\ \text{m} east