Distance is the total length of the path an object actually travels. It is a scalar — a number with a unit and nothing else, no direction attached. If you walk 60 meters down a hallway, distance says 60 m. If you then walk back 40 meters, distance doesn't care that you reversed course — it just keeps adding.
Because distance only ever accumulates, it can never be negative and it can never decrease over time. Every step you take — forward, backward, sideways, in circles — adds to it.
Displacement only compares your final position to your starting position. It is the straight-line change in position:
Displacement is a vector — it has both size and direction. On a one-dimensional number line, direction shows up as a sign: positive means net motion one way, negative means net motion the other way. (You'll formalize signed direction in Lesson 1-1-3 — for now, just notice that Δx can come out positive, negative, or zero depending on where x_i and x_f fall.)
You start at position x_i = 5 m along a hallway, walk to x = 45 m, then walk back to x_f = 30 m. Find the total distance traveled and the displacement.
The single most common error with these two quantities: assuming distance and displacement are always the same number, or assuming that "no displacement" means "no motion happened." Neither is true.
Set a start position, a turnaround point, and a final position along a number line (in meters). Watch how distance and displacement respond independently.
Try setting x_final equal to x_start — displacement drops to zero while distance stays large and positive. That's the round-trip case in action.
A cyclist starts at x_i = 0 m, rides out to x = 60 m, then rides back to x_f = 20 m. Find the distance, the displacement, and identify which one changed.
Speed is a rate: how much distance is covered per unit of time. Because it's built from distance (a scalar) and time (always positive), speed is also a scalar — no direction attached.
Average speed treats the entire trip as one lump sum. It doesn't matter if you sprinted for part of the trip and crawled for another part — average speed only sees the total distance and the total time elapsed.
A hiker walks 3.0 km out to a lookout in 40 minutes, then walks back along the same trail in 30 minutes. Find her average speed for the entire hike.
You now have three tools: distance, displacement, and speed. There's a fourth idea waiting just around the corner — velocity, which is to displacement what speed is to distance: a rate, but this time a rate built from a vector. Average velocity = Δx / Δt.
distance, average speed — magnitude only, never negative
displacement, velocity — magnitude AND direction, signed numbers