Physics / Unit 1: Motion in One Dimension
1.1 Position, Distance and Displacement
Notes
Position is where an object is compared to a chosen reference point (the origin). Choose a positive direction and stick with it.
- Distance is the total length of the path traveled. It is a scalar (size only) and is never negative.
- Displacement is the change in position: $\Delta x = x_f - x_i$. It is a vector (size and direction) and can be negative.
- If you end where you started, your displacement is zero even if the distance is large.
- Example: walk 5 m east, then 2 m west. Distance $= 7 \text{ m}$; displacement $= 3 \text{ m}$ east.
Practice
A runner does one full lap of a 400 m track and stops at the starting line. What is her displacement?
She ends where she began, so the change in position is zero.
A car moves from $x = 12 \text{ m}$ to $x = 4 \text{ m}$. What is its displacement?
$\Delta x = x_f - x_i = 4 - 12 = -8 \text{ m}$; the negative sign shows direction.
A dog walks 6 m north and then 6 m south. Which statement is true?
Distance adds up the whole path; the dog ends at its starting point.
Ready for more? Take the Unit 1 test.