AcademyOne-Dimensional Motion
Academy
Position and Time
Level 1 - Physics topic page in One-Dimensional Motion.
Principle
Position locates an object on a chosen axis at a stated time. The number only has meaning after an origin, a positive direction, and a clock reading have been chosen.
Notation
\(x\)
position on the axis
\(\mathrm{m}\)
\(t\)
time
\(\mathrm{s}\)
\(x_0\)
initial position
\(\mathrm{m}\)
\(\Delta x\)
displacement
\(\mathrm{m}\)
\(\Delta t\)
elapsed time
\(\mathrm{s}\)
Method
Displacement
\[\Delta x = x_f - x_i\]
Subtract positions measured from the same origin.
Elapsed time
\[\Delta t = t_f - t_i\]
Use the same clock for both times.
Axis sign
\[x < 0 \quad \text{means opposite the chosen positive direction}\]
The graph below represents a motion as a sequence of time-position states. Read position from a single point, and read displacement from the change between two points.
The graph gives net changes in position. It does not determine total distance unless the path between recorded states is known.
Rules
These are the compact results from the method above.
Displacement
\[\Delta x = x_f - x_i\]
Elapsed time
\[\Delta t = t_f - t_i\]
Position function
\[x = x(t)\]
Examples
Question
A particle moves from
\[x_i=-2\,\text{m}\]
to \[x_f=5\,\text{m}\]
What is its displacement?Answer
\[\Delta x=x_f-x_i=5-(-2)=7\,\text{m}\]
The positive sign means the displacement is in the positive axis direction.Checks
- Position depends on origin.
- Displacement does not equal distance.
- Signs must match the axis.
- Time intervals are usually positive.