Displacement Examples in Math

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Displacement.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Math.

Concept Recap

The straight-line change in position from start to end, with both a distance and a direction.

Where you ended up relative to where you started—direction and distance combined.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Displacement is a vector; distance traveled is a scalar (might be longer).

Common stuck point: Walking in a complete circle covers a large distance traveled, but your net displacement is exactly zero.

Sense of Study hint: Draw your start point and end point. The straight arrow between them is your displacement, ignoring the winding path you took.

Worked Examples

Example 1

easy
A person walks 5 m east and then 5 m west. What is their displacement?

Solution

  1. 1
    Step 1: Represent east as positive x and west as negative x.
  2. 2
    Step 2: Displacement = +5 + (-5) = 0 m.
  3. 3
    Step 3: The person is back at their starting point — zero displacement.

Answer

Displacement = 0 m (back to start).
Displacement is the straight-line vector from the starting point to the ending point. It depends only on start and end positions, not the path taken. Total distance walked was 10 m, but displacement was 0 — an important distinction.

Example 2

medium
A robot moves from point A(1, 2) to point B(4, 6). Find the displacement vector and its magnitude.

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
A car drives 3 km north, then 4 km east. What is the magnitude of the total displacement?

Example 2

hard
A particle undergoes three displacements: \vec{d_1} = (2, -1), \vec{d_2} = (-3, 4), \vec{d_3} = (1, 2). Find the net displacement vector and its magnitude.
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Background Knowledge

These ideas may be useful before you work through the harder examples.

vector intuition