Physics · Class 11

Distance & displacement

Position states where the walker is relative to an origin. Displacement is final position minus starting position. Distance adds the lengths of all travelled parts. Reversing direction can cancel displacement while distance continues to increase.

Open the interactive experiment →

A return journey can have zero displacement.

இடப்பெயர்ச்சி இறுதி நிலையிலிருந்து தொடக்க நிலையை கழித்த மதிப்பு. கடந்த தொலைவு பாதையின் எல்லாப் பகுதிகளின் நீளங்களையும் கூட்டும். திரும்பி வந்தாலும் தொலைவு பூஜ்யமாகாது.

Key notes, relationships and model limits

Key relationship

Δx = v₁t₁ + v₂t₂; distance = |v₁|t₁ + |v₂|t₂

Remember

Common trap

Distance equals the magnitude of displacement only when direction does not reverse.

Model limits

Straight route; constant velocity on each leg; ideal instantaneous velocity change at the selected time. Right is positive.

What you will learn

Distinguish position, signed displacement and nonnegative distance in a route with a reversal.

Try the experiment

Scrub past the velocity-change time. Set opposite velocities, then try a route that returns exactly to its start.

Think of it this way

Walking from home to a shop and back adds walking distance while returning your location to home.

Worked example

At +4 m/s for 5 s, then −4 m/s for 5 s, Δx = 20 − 20 = 0 m and distance = 20 + 20 = 40 m.

Why this matters

Distance helps estimate effort and journey length; displacement locates the endpoint.

Before you start

Signed numbers · coordinates · gradients · area under a graph

Check your understanding

A person walks 20 m right, then 20 m left. What are distance and displacement?

0 m and 40 m
40 m and 0 m
20 m and 20 m

Read the explanation

Distance = 20 + 20 = 40 m. Displacement = +20 − 20 = 0 m.

Course connection: CBSE XI Chapter 2; NEET and JEE Main Unit 2; JEE Advanced Mechanics. Check the selected syllabus for relative-velocity scope.