Position vector, displacement and distance

Motion along a straight line

• We describe motion of a particle on a line with all quantities written in terms of the time t.
• The position vector r(t) locates the particle from the origin; its magnitude is measured in units of length. We use s (or x) for the algebraic measure of the position, so its sign gives the side of the origin.
• The displacement vector is the change of position between two instants: s = r(t₂) − r(t₁).
• Distance is the actual length of the path travelled; it is scalar and is never negative, whereas displacement may be positive, negative or zero.
• A body that returns to its starting point has zero displacement but non-zero distance.

Point of comparison	Displacement	Distance
Type of quantity	Vector	Scalar
Sign	positive, negative or zero	always positive (or zero)
Depends on	only the initial and final points	the whole path