Position, Reference Points, and Rest
Position is the location of an object relative to a chosen reference point (the origin), and an object is at rest when its position does not change with time relative to that reference point. In brief: motion is always described relative to something else, so “at rest” and “moving” depend on the reference frame. Position on a straight line is given by a signed number x, and the change in position, Δx = xfinal − xinitial, is the displacement.
A passenger sitting on a train is at rest relative to the seat, but moving at 30 m/s relative to the station. Before any motion can be calculated, we must say what it is measured against. This guide defines position and reference points, explains coordinate systems and rest, compares different frames in a table, works through an example on a number line and corrects common mistakes.
What is position?
The position of an object tells where it is. In one dimension (a straight road or a track), a number line is used: the origin is x = 0, one direction is positive and the opposite is negative. A position of x = −3 m means 3 m on the negative side of the origin. In two dimensions, two coordinates (x, y) are used, and in three dimensions three (x, y, z). The position can also be given as a distance and direction from the reference point, such as 200 m north of the school.
When describing the motion of an object, it is often treated as a point object if its size is small compared with the distances involved. A car on a trip between two cities can be treated as a point, but the same car turning in a parking lot cannot.
What is a reference point?
A reference point (origin) is the place chosen as the zero of position. A frame of reference is a reference point together with the axes and a clock that are used to describe the position at each instant. You can choose any frame, but a convenient choice makes the problem simpler: for a ball thrown up, the ground is a natural origin with upward as positive.
The values of position depend on the choice of the origin, but the displacement between two positions does not. If an object moves from x = 2 m to x = 7 m, the displacement is 5 m, whether the origin is at a wall or a tree.
What does rest mean?
An object is at rest when its position relative to the chosen reference point does not change as time passes. An object is in motion when its position changes. There is no absolute rest: a house is at rest relative to the Earth, but moves with the Earth around its axis (about 465 m/s at the equator) and around the Sun (about 30 km/s). In everyday physics, the Earth’s surface is usually the reference frame, and objects at rest are those that do not change position with respect to the ground.
Reference frames compared
| Object | Reference frame | State |
|---|---|---|
| Passenger on a train | The train seat | At rest |
| Passenger on a train | The station platform | Moving with the speed of the train |
| Tree beside the track | The ground | At rest |
| Tree beside the track | The train | Moving backward |
Worked example: position and displacement on a line
A toy car moves along a straight track. A school wall is chosen as the origin (x = 0), and the positive direction points to the right. The car starts at x = −2.0 m, moves to x = +5.0 m and then back to x = +1.0 m.
- First displacement: Δx1 = 5.0 − (−2.0) = +7.0 m (7.0 m to the right).
- Second displacement: Δx2 = 1.0 − 5.0 = −4.0 m (4.0 m to the left).
- Total displacement: Δx = 1.0 − (−2.0) = +3.0 m. As a check, 7.0 + (−4.0) = +3.0 m.
- Total distance traveled: 7.0 m + 4.0 m = 11.0 m.
If the origin were moved 2.0 m to the left, all the positions would increase by 2.0 m (0 m, 7.0 m and 3.0 m), but the displacements and distance would be the same.
How did the idea of relative motion develop?
Aristotle believed that the Earth is at rest at the center of the universe. Nicolaus Copernicus proposed in 1543 that the Earth moves around the Sun, and Galileo argued in 1632, in his Dialogue Concerning the Two Chief World Systems, that a person inside a ship cannot tell by experiments whether the ship is at rest or moving uniformly. This is the principle of relativity, which Einstein extended in 1905.
Which mistakes are common?
Mistake 1: Saying that an object is at rest without a reference
Rest and motion are relative. Always say relative to what.
Mistake 2: Confusing position and displacement
Position depends on the origin. Displacement is the change in position.
Mistake 3: Ignoring signs on a number line
A negative position or displacement shows direction, and it is not an error.
Mistake 4: Thinking that a body at rest has no forces acting on it
An object at rest may have balanced forces acting on it, such as a book on a table (weight and normal force).