Displacement Examples in Physics

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 Physics.

Concept Recap

The change in position from a starting point to an ending point, including both magnitude and direction.

How far you are from where you started, in a straight line. Not the path you took.

Read the full concept explanation โ†’

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 only depends on start and end points โ€” the path taken doesn't matter.

Common stuck point: Displacement is a vector with direction; distance is a scalar that is always positive.

Worked Examples

Example 1

easy
A person walks 4 \text{ m} east and then 3 \text{ m} north. What is the total distance traveled and the displacement?

Solution

  1. 1
    Total distance traveled is the sum of path lengths: d = 4 + 3 = 7 \text{ m}.
  2. 2
    Displacement is the straight-line distance from start to finish: |\vec{d}| = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5 \text{ m}
  3. 3
    Direction: \theta = \tan^{-1}\left(\frac{3}{4}\right) \approx 36.9ยฐ north of east.

Answer

\text{Distance} = 7 \text{ m}, \quad \text{Displacement} = 5 \text{ m at } 36.9ยฐ \text{ N of E}
Displacement is a vector quantity measuring the shortest path from start to end point, while distance is the total path length traveled. They differ whenever the path is not a straight line.

Example 2

medium
A runner completes one full lap around a 400 \text{ m} circular track. What is the runner's displacement and total distance?

Practice Problems

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

Example 1

easy
A car drives 100 \text{ m} north and then 100 \text{ m} south. What is the displacement?

Example 2

medium
A hiker walks 3 \text{ km} north, then 4 \text{ km} east. What is the hiker's total distance walked and their displacement (magnitude and direction)?

Related Concepts

Background Knowledge

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

position