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.
Key Formula
x = x0 + Δx
LaTeX: x = x_0 + \Delta x
| Symbol | Meaning | Unit |
|---|---|---|
| x | Current position | m |
| x₀ | Initial position (origin) | m |
| Δx | Change in position (displacement) | m |
Worked Example
Problem
A car starts at a position of 10 m from a lamp post and moves to 35 m from the same lamp post. What is its final position, and what is the displacement?
Solution
Step 1: Identify the reference point — the lamp post at x = 0 m. Step 2: Initial position x₀ = 10 m. Step 3: Final position x = 35 m. Step 4: Displacement Δx = x − x₀ = 35 − 10 = 25 m.
Answer
Final position = 35 m; Displacement = 25 m (in the positive direction).
Position in one, two, and three dimensions
| Dimension | Coordinates used | Example | SI Unit |
|---|---|---|---|
| 1D (line) | x | Car on a straight road | m |
| 2D (plane) | x, y | Ship on the ocean surface | m |
| 3D (space) | x, y, z | Aircraft in flight | m |
| Polar (2D) | r, θ | Satellite orbit in a plane | m, rad |
| Spherical (3D) | r, θ, φ | Planet around the Sun | m, rad |
Interactive Tools
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Related Terms
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).
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).
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.
From Latin "positio" (a placing, position), derived from "ponere" (to place). Entered scientific use in the 17th century as Newtonian mechanics formalised the description of location in space.