Distance vs Displacement, Velocity vs Speed

When an object moves, we can describe its motion using two different measurements: displacement and distance. These concepts tell us very different things about motion.

What is Displacement?

Displacement measures the change in position from start to finish. It includes both:

• Magnitude: how far the final position is from the starting position
• Direction: which way the object ended up relative to where it started

Displacement only cares about your starting point and ending point—nothing in between matters.

What is Distance?

Distance measures the total length of the path traveled. It:

• Only has magnitude (no direction)
• Adds up every bit of motion, regardless of which way you moved
• Is always positive or zero

A Simple Example

Imagine you walk $10$ meters east, then turn around and walk $10$ meters west.

• Displacement: $0$ meters (you're back where you started)
• Distance: $20$ meters (you walked a total of $20$ meters)

Horizontal Motion Example

Let's look at an object that starts at position $x_0 = -5 \text{ m}$ and makes three moves:

• Move 1: $\Delta x_1 = 15\text{ m}$ (moves right)
• Move 2: $\Delta x_2 = -8\text{ m}$ (moves left)
• Move 3: $\Delta x_3 = 6\text{ m}$ (moves right)

Calculating Displacement

To find the total displacement, we add up all the individual displacements (keeping track of direction):

The final position is: