Physics · Class 11

Reference frames

Position and velocity need an observer. The roadside origin stays at x = 0. The bus origin moves at the bus velocity, so its coordinates subtract the bus displacement. Both descriptions refer to the same walker at the same time.

Open the interactive experiment →

Describe the same journey from two observers.

நிலை மற்றும் திசைவேகம் பார்வையாளரைச் சாரும். பேருந்தின் இடப்பெயர்ச்சியை சாலை நிலையில் இருந்து கழித்தால் பேருந்து சார்ந்த நிலை கிடைக்கும்.

Key notes, relationships and model limits

Key relationship

x′ = x − vbus t; v′ = v − vbus

Remember

Common trap

A negative velocity in the bus frame does not imply a negative velocity on the road.

Model limits

One dimension; constant bus and walker velocities; origins coincide at t = 0; clocks agree. The bus frame is inertial.

What you will learn

Transform positions and velocities between the roadside and a uniformly moving bus.

Try the experiment

Play the journey, switch observers, then try equal bus and walker velocities. Compare both coordinate lines.

Think of it this way

A person beside your moving bus can seem to move backward even while walking forward along the road.

Worked example

With x0 = 10 m at t = 5 s, the walker is at 20 m on the road. The bus origin is at 30 m, so the walker is at x′ = −10 m.

Why this matters

An explicit observer prevents contradictory descriptions of a single event.

Before you start

Signed numbers · coordinates · gradients · area under a graph

Check your understanding

A walker moves at +2 m/s and the bus at +6 m/s on the road. What is the walker velocity seen from the bus?

+8 m/s
−4 m/s
+4 m/s

Read the explanation

Subtract the observer velocity: v′ = 2 − 6 = −4 m/s. The walker falls behind the bus.

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