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Position, Displacement & Distance

Welcome to Physics!

Let's start by learning how to describe motion precisely

Before we can analyze motion, we need a precise language to describe it. In everyday life, we use words like 'far' or 'fast' - but in physics, we need exact definitions.

The first step is understanding the difference between position, displacement, and distance.

Distance vs Displacement
Understanding the difference between path length (distance) and net change in position (displacement)

Illustration: displacement-vector

Position
Position
x or r
Where an object is located relative to a chosen reference point (origin). Position is a vector - it has both magnitude and direction.
x:
Position along one axis (1D motion)

r:
Position vector (2D or 3D motion)

origin:
The reference point where x = 0

💡
The Address Analogy

Think of position like a street address. '123 Main St' tells you exactly where something is relative to a reference (the start of Main St).

Your position changes when you move. If you walk from 123 Main St to 456 Main St, your position changed from x = 123 to x = 456.

Displacement vs Distance
Displacement
Δx = x_final - x_initial
The change in position - how far you ended up from where you started, in a straight line. Displacement is a vector.
Distance vs Displacement
Easy
You walk 3 km east, then 4 km west. Find your distance traveled and displacement.
1
Calculate distance
Distance = total path length = 3 km + 4 km = 7 km
2
Calculate displacement
Take east as positive: Displacement = +3 km + (-4 km) = -1 km You ended up 1 km west of where you started.
Answer: Distance = 7 km, Displacement = 1 km west
💡 You traveled 7 km total, but only ended up 1 km from your starting point!

Quick Check

1. A car drives 100 m north, then 100 m south, returning to its starting point. What is its displacement?
200 m
100 m north
0 m
100 m south
Key Takeaways

  • Position tells you where an object is relative to an origin

  • Distance is total path length (always positive)

  • Displacement is change in position (can be positive, negative, or zero)

  • Displacement = final position - initial position