What Are Distance and Displacement?
Distance and displacement both describe motion, but they answer different questions. Distance is the total path length traveled, while displacement is the straight-line change in position from start to finish, including direction.
Distance is a scalar — the total length of the path traveled. Displacement is a vector — the straight-line distance and direction from the starting point to the ending point.
- •Scalar quantity — magnitude only, no direction
- •Total length of the actual path traveled
- •Always positive, never decreases as you move
- •Measured like an odometer path length
- •Vector quantity — has both magnitude and direction
- •Straight-line distance from start to end point
- •Can be zero even if distance traveled is large (e.g., a round trip)
- •Measured as the shortest path between two points
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Step-by-step worked examples
A runner completes one full lap of a 400 m circular track, ending where they started. Find the distance and displacement.
Distance = total path length = 400 m Displacement = final position − initial position = 0 m (same start/end point)
A person walks 3 m east, then 4 m north. Find the distance and displacement.
Distance = 3 + 4 = 7 m (sum of path segments) Displacement = √(3² + 4²) = √25 = 5 m (northeast direction)
A car drives 10 km north, then 6 km south. Find the distance and displacement.
Distance = 10 + 6 = 16 km Displacement = 10 − 6 = 4 km north (net change in position)
Flashcards
Quick quiz
Q1.Which of the following is a vector quantity?
Q2.A person walks 5 m forward and then 5 m back to the start. What is their displacement?
Q3.A hiker walks 6 m east and 8 m north. What is the magnitude of the displacement?
Q4.Which statement is always true?
The full card deck, worked steps and AI-tutor support for “What Are Distance and Displacement?” are in Notek — study by hand before your exam.
Common mistakes
Distance and displacement are always the same. — Correct: They're equal only for straight-line motion in one direction with no backtracking; otherwise distance ≥ displacement.
Displacement can't be negative or have a sign. — Correct: Displacement is a vector and can be negative depending on the chosen direction convention.
Distance can be negative if you go backward. — Correct: Distance is always positive — it's a total path length, direction doesn't subtract from it.
If displacement is zero, no motion occurred. — Correct: The object may have moved a large distance but ended up back at the starting point, giving zero displacement.
FAQ
What is the difference between distance and displacement?
Distance is the total scalar path length traveled; displacement is the vector straight-line change in position, including direction.
What is the formula for displacement?
For 2D motion, displacement magnitude is d = √(Δx² + Δy²), the straight-line distance between start and end points.
What are examples of distance and displacement?
A runner finishing a lap: distance = the full lap length, displacement = 0. Walking 3 m east then 4 m north: distance = 7 m, displacement = 5 m.
How do you calculate displacement when direction changes?
Break the motion into x and y components, sum each direction separately, then use d = √(Δx² + Δy²) to find the resultant.