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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.

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