Displacement
Displacement is the shortest straight-line distance between an object's initial and final positions, measured as a vector quantity with both magnitude and direction. Unlike distance, displacement does not account for the actual path taken, only the net change in position. It is the fundamental quantity used to define velocity and is measured in metres (m).
Key Formula
s = r_final − r_initial
LaTeX: \vec{s} = \vec{r}_f - \vec{r}_i
| Symbol | Meaning | Unit |
|---|---|---|
| s⃗ | Displacement vector | m |
| r⃗_f | Final position vector | m |
| r⃗_i | Initial position vector | m |
Worked Example
Problem
A student walks 8 m east and then 6 m north. What is the magnitude of the student's displacement from the starting point?
Solution
Step 1: Set up a coordinate system: east = +x, north = +y. Step 2: Initial position = (0, 0); Final position = (8, 6) m. Step 3: Displacement vector s⃗ = (8 − 0, 6 − 0) = (8, 6) m. Step 4: Magnitude |s⃗| = √(8² + 6²) = √(64 + 36) = √100 = 10 m.
Answer
Displacement = 10 m at an angle of arctan(6/8) ≈ 36.87° north of east.
Displacement vs. Distance comparison
| Property | Displacement | Distance |
|---|---|---|
| Type | Vector | Scalar |
| Depends on path? | No — only start and end | Yes — full path length |
| Can be zero? | Yes (if start = end) | No (unless no motion) |
| Can be negative? | Yes (direction dependent) | No |
| SI Unit | metre (m) | metre (m) |
| Symbol | s or Δx | d |
Interactive Tools
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Related Terms
Position
Position is the location of an object in space relative to a chosen reference point, described by a set of coordinates. It is a fundamental concept in mechanics because all motion is defined as a change in position over time. In one dimension, position is typically denoted by x and measured in metres from the origin.
Distance
Distance is the total length of the path travelled by an object, regardless of direction. It is a scalar quantity, meaning it has magnitude only and is always non-negative. Distance differs from displacement because it tracks the entire route rather than the straight-line separation between start and finish.
Velocity
Velocity is the rate of change of displacement with respect to time, making it a vector quantity with both magnitude (speed) and direction. Average velocity equals total displacement divided by total time, while instantaneous velocity is the derivative of position with respect to time. Velocity is central to Newton's laws and is measured in metres per second (m/s).
From Latin "displacere" — "dis-" (away) + "placere" (to place). The word entered physics usage in the 18th century to describe the net shift in position rather than the route travelled.