Mini Physics
Part of Mini EducationSwitch subject
Search

Distance vs Displacement

Key idea: Learn distance vs displacement (scalar vs vector), including direction, sign conventions, and exam-style worked examples for O Level Physics.

  • SEC G3 Physics 2027
On this page

Learning objectives

  • State what speed means
  • State what velocity means, including its direction
  • Calculate average speed from total distance and total time
  • Calculate acceleration as change in velocity divided by time taken
  • State what uniform acceleration means
  • Interpret examples of non-uniform acceleration
  • Plot and interpret displacement–time and velocity–time graphs in one dimension
  • Deduce rest and uniform or non-uniform velocity from a displacement–time graph
  • Deduce rest, uniform velocity and uniform or non-uniform acceleration from a velocity–time graph
  • Use signed area under a velocity–time graph to determine displacement
  • Recall constant free-fall acceleration near Earth as approximately 10 m/s²

1. Definition

A. Distance (distance travelled)

Distance travelled is the total length of the path taken, regardless of direction.

B. Displacement

Displacement is the change in position from the initial point to the final point, in a stated direction. Its magnitude is the straight-line separation between those points.

2. Key Ideas

  • Both distance and displacement have SI unit m (see Base Quantities & SI Units).
  • Distance is a scalar (no direction) (see Scalar & Vector Quantities) and is always ≥ 0.
  • Displacement is a vector (has direction) (see Scalar & Vector Quantities) and can be positive, negative, or zero (depending on your chosen direction).
  • Always true: distance travelled ≥ magnitude of displacement.
  • Distance depends on the path taken; displacement depends only on the start and end positions.
  • Link to next lesson:
    • speed uses distance: speed = distance / time
    • velocity uses displacement: velocity = displacement / time

Distance travelled vs displacement (same journey)

Two lines show how distance travelled always increases while displacement can decrease if the object moves back towards the start.

Scroll across the graph to read all labels.

Two lines show how distance travelled always increases while displacement can decrease if the object moves back towards the start.Two lines show how distance travelled always increases while displacement can decrease if the object moves back towards the start.
Displacement can decrease (if you move back), but distance travelled cannot decrease because it is the total path length.
Open full-size graph
View figure data
Values for Distance travelled vs displacement (same journey)
Time (s)Displacement (signed)Distance travelled (total)
000
122
244
326
408

3. Detailed Explanations

A. Visual meaning (path vs straight line)

Distance and displacement for the same journeyA winding route from point A to point B is labelled distance travelled. A straight arrow from A to B is labelled displacement and points north-east.One journey, two quantitiesA · startB · finishdistance travelledlength of the complete routedisplacementstraight arrow, north-east
Scroll diagram horizontally to read all labels.
Distance follows the whole route and has magnitude only. Displacement joins the start to the finish and requires both magnitude and direction.
  • If an object moves from B to C to D:
    • distance travelled = BC + CD
    • displacement = BD (from B to D)

B. When are distance and displacement equal?

Distance travelled equals the magnitude of displacement only when:

  • the object moves in a straight line, and
  • it does not change direction.

C. Zero displacement does not mean zero distance

If an object returns to where it started, then:

  • displacement = 0
  • distance travelled is usually not zero (unless it didn’t move at all)

D. Positive and negative displacement (1D)

To decide whether displacement is positive or negative, you must choose a positive direction (e.g. “to the right is positive”).

Example:

  • Move 3 m to the right: displacement = +3 m.
  • Move 3 m to the left: displacement = -3 m.

E. Summary table (exam-friendly)

FeatureDistance travelledDisplacement
Meaningtotal path lengthstraight-line change from start to end (with direction)
Typescalarvector
Can be negative?noyes (depends on direction chosen)
Can be zero?yes (no motion)yes (returns to start)
Depends on path?yesno
Key checkdistance travelled ≥ magnitude of displacementdistance travelled ≥ magnitude of displacement

4. Common Mistakes

A. Concept mix-ups

  • Giving distance when the question asks for displacement (or vice versa).
  • Writing displacement without direction (e.g. “5 m” instead of “5 m east”).
  • Thinking displacement means “distance from the starting point along the path” (it is the straight line).

B. Sign and “zero” mistakes

  • Writing distance as negative.
  • Saying “displacement is zero, so distance is zero” (false).
  • Not stating the chosen positive direction in 1D questions.

5. Exam Tips

A. Quick checks for marks

  • Write definitions using exam keywords:
    • distance: “total length of path”
    • displacement: “shortest straight line from start to end, with direction”
  • For multi-leg journeys: draw a quick sketch and mark the start and end points.
  • Use the sanity check: distance travelled ≥ magnitude of displacement.
  • If a question is 1D, state the sign convention (e.g. “right is positive”).
  • If the object ends where it started, write displacement = 0 immediately, then compute distance from the full path.

6. Worked Examples

Modelled example 1

L-shaped path (distance vs displacement)

Core

Problem

Ali walks 1 km north, 1 km east and 1 km south. Find the distance travelled and displacement.
Study the worked solution

  1. Add the complete path

    Method

    Add the lengths of all three legs without cancelling direction.

    Reason

    Distance travelled is the total path length and is scalar.

    Working

    d = 1 + 1 + 1 = 3 km

  2. Find the net change in position

    Method

    Combine the directed north–south changes, then retain the remaining eastward change.

    Reason

    Displacement depends only on start and finish, with direction.

    Working

    The 1 km north and south legs cancel, leaving 1 km east.

Guided practice 2

Curved path vs straight-line displacement

About 4 min

Problem

Use the journey diagram above. An object follows the curved route from A to B. State what represents the distance travelled and what represents the displacement.

Identify each representation

Distance travelled
Displacement

Hints

Hint 1: follow the travelled route
The scalar quantity accumulates every part of the path.
Hint 2: connect start directly to finish
The vector quantity uses the straight start-to-end arrow and its direction.
View solution step by step

  1. Identify the path quantity

    Method

    Use the length of the complete curved route for distance travelled.

    Reason

    Distance depends on the path actually taken.

    Working

    Trace the route from A to B and add its full length.

  2. Identify the start-to-finish vector

    Method

    Use the straight arrow from A to B with its north-east direction.

    Reason

    Displacement ignores the intervening curve and records only the change in position.

    Working

    Displacement is the directed straight-line separation A → B.

Common misconception 3

Can displacement be larger than distance?

Find and correct the mistake

Learner response

A learner says a shortcut can make the magnitude of displacement greater than the distance travelled because displacement “ignores the bends”. Locate the first conceptual error and correct the claim.

Diagnose before viewing the correction

First error

View solution step by step

  1. Use the geometric bound

    Method

    Compare the actual path with the straight start-to-end line.

    Reason

    The straight line is the shortest separation between the endpoints.

    Working

    Any bends can only make the travelled path equal to or longer than the displacement magnitude.

  2. State the invariant

    Method

    Write the correct inequality.

    Reason

    It must hold for every journey.

    Working

    distance travelled ≥ |displacement|

Examiner practice 4

1D motion (use absolute values for distance)

4 marks

Examination question

A particle starts at x = 2 m, moves to x = -5 m, then moves to x = 1 m. Find the distance travelled and displacement. [4 marks]

Show both leg lengths and the signed change

View solution step by step

  1. Calculate both path legs

    2 marks

    Method

    Use absolute position changes for each travelled leg.

    Reason

    Distance accumulates non-negative path lengths even when direction reverses.

    Working

    d = |-5-2| + |1-(-5)| = 7 + 6 = 13 m

  2. Calculate the signed displacement

    2 marks

    Method

    Subtract initial position from final position.

    Reason

    Only the endpoints determine displacement.

    Working

    Δ x = x_f-xᵢ = 1-2 = -1 mThe final position is 1 m in the negative direction from the start.

Challenge 5

One full lap (displacement can be zero)

Minimal support

Closed-path transfer

An athlete runs one full lap of a 400 m track and finishes at the starting point. Find the distance travelled and displacement, then explain why the two answers differ.

Try the closed-path case

Unit: m
Unit: m

Hints

Hint 1: separate path from endpoints
One quantity accumulates the lap; the other compares start and finish.
View solution step by step

  1. Use the path length

    Method

    Count the full lap as distance travelled.

    Reason

    The athlete moves along all 400 m of the track.

    Working

    Distance travelled = 400 m.

  2. Compare start and finish

    Method

    Use the zero change in position.

    Reason

    The athlete finishes exactly where the journey began.

    Working

    Displacement = 0 m.

7. Mind Stretchers

Mind stretcher 1: A classic Pythagoras caseExtension

A student walks 3 m east then 4 m north.

  1. Find the distance travelled.
  2. Find the magnitude of displacement.
Show Answer
  • Distance travelled: 3 + 4 = 7 m
  • Magnitude of displacement: square root of (3² + 4²) = 5 m

Mind stretcher 2: “If displacement is zero, distance is zero.” True or false?Extension

Decide whether this statement is true or false, and explain.

Show Answer

False. Displacement can be zero if you return to your starting point, but you may have travelled a non-zero distance along the path.

Continue with the next resource in this course.

Course and syllabus information
Course
SEC G3 Physics
Edition
SEC G3 Physics 2027