Reference Frame Examples in Physics

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

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

Concept Recap

A coordinate system used to describe positions and motions, relative to an observer.

Are you 'moving' on a train? Depends on whether you ask someone on the train or the platform.

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: Motion is always relative — you must specify which reference frame you're measuring from.

Common stuck point: There's no special reference frame—all inertial frames are equally valid.

Worked Examples

Example 1

easy
Train A moves east at 30 \text{ m/s} and Train B moves east at 20 \text{ m/s}, both relative to the ground. What is the velocity of Train A relative to Train B?

Solution

  1. 1
    The velocity of A relative to B is: v_{AB} = v_A - v_B.
  2. 2
    v_{AB} = 30 - 20 = 10 \text{ m/s east}
  3. 3
    From the perspective of a passenger on Train B, Train A appears to move east at 10 \text{ m/s}.

Answer

v_{AB} = 10 \text{ m/s east}
A reference frame is a viewpoint from which motion is observed. Relative velocity between two objects is found by subtracting their velocities. Different observers can measure different velocities for the same object.

Example 2

medium
A boat travels at 5 \text{ m/s} relative to the water, heading directly across a river that flows at 3 \text{ m/s}. What is the boat's speed relative to the ground, and at what angle does it actually travel?

Practice Problems

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

Example 1

medium
Car A travels north at 25 \text{ m/s} and Car B travels south at 20 \text{ m/s}, both relative to the ground. What is the velocity of Car A as seen by Car B?

Example 2

hard
A plane flies at 250 \text{ m/s} due north relative to the air. A wind blows at 50 \text{ m/s} from the west (toward the east). What is the plane's ground speed and actual direction of travel?
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Related Concepts

PositionVelocityInertia

Background Knowledge

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

positionvelocity