Position can be understood as the location of an object with respect to a reference point. It is expressed as a position vector.
Shown below is the position of a cyclist with respect to a lamp post. Cyclist starts at the lamp post and goes to Position 1, 2, 3 and 4 respectively.
Position 1, P1→ = +3 units
Position 2, P2→ = +5 units
Position 3, P3→ = -2units
Position 4, P4→ = -6units
It is interesting to observe that the final displacement vector is the same as the final position vector. This is because,
P1→ + P2→ + P3→ + P4→
D→ = 3 + 2 - 7 - 4 = -6 units
Displacement between two positions starting at PA→ and ending at PB→ is defined as −
Displacement, D→ = PB→ - PA→
For Example, in the figure below,
Displacement between position 2 and position 4,
D→ = P4→ - P2→ = -6 - (+5) = -11 units
The magnitude of Displacement may or may not be equal to Distance.
For example, in the figure below,
Between P1→ and P2→ −
Distance = 2 units
Magnitude of displacement = |+5 - (+3)| = 2 units
Between P1→ and P3→ −
Distance = 9 units
Magnitude of displacement = |-2 - (+3)| = 5 units
- If the object doesn’t change direction during motion, distance is equal to magnitude of displacement. (as evident between P1→ and P2→)
If the object changes direction during motion, distance is always greater than displacement. (as evident between P1→ and P3→)