1. What Is Relative Velocity?
Relative velocity explains how fast one object appears to be moving as seen from another moving object. Motion looks different to different observers depending on their own motion.
For example, a person sitting inside a bus feels another passenger is at rest, but someone standing on the road sees both passengers moving.
1.1. Why Motion Looks Different to Different Observers
Motion is always described relative to something else. If the observer is also moving, the same motion can appear slower, faster, or even zero.
2. Basic Idea of Relative Velocity
To understand relative velocity, imagine comparing the velocities of two objects. We subtract one velocity from another to find how fast one object seems to move with respect to the other.
2.1. General Formula
The formula for relative velocity of object A with respect to object B is:
\( v_{AB} = v_A - v_B \)
This means we subtract the velocity of B from the velocity of A.
2.2. Understanding the Formula
If both objects are moving in the same direction, the relative velocity becomes smaller. If they move in opposite directions, the relative velocity becomes larger.
3. Relative Velocity in the Same Direction
When two objects move in the same direction, the difference between their speeds decides how fast one appears to be moving relative to the other.
3.1. Example
If car A is moving at 60 km/h and car B is moving ahead of it at 50 km/h in the same direction:
\( v_{AB} = 60 - 50 = 10 \text{ km/h} \)
Car A appears to approach car B at just 10 km/h, even though its actual speed is 60 km/h.
4. Relative Velocity in Opposite Directions
When two objects move in opposite directions, their velocities add up.
4.1. Example
If two bikes approach each other, one at 40 km/h and the other at 30 km/h:
\( v_{AB} = 40 - (-30) = 70 \text{ km/h} \)
They seem to be approaching each other at a speed of 70 km/h.
5. Relative Velocity in Situations Around Us
Many everyday situations involve relative velocity, even if we don't think about it consciously.
5.1. Examples
- A passenger inside a train seeing another train pass by.
- A person walking inside a moving bus.
- Cars overtaking each other on a highway.
- Boats crossing a river while water flows.
6. Relative Velocity of Trains (Classic Example)
Trains offer the easiest way to understand relative velocity.
6.1. Example
If you are sitting in a train moving at 70 km/h and another train beside you moves at 70 km/h in the same direction, the other train appears stationary:
\( v_{AB} = 70 - 70 = 0 \)
7. Key Points to Remember
Relative velocity tells us how fast one object appears to move from another object. It depends on the observer's own motion and the direction of movement.
7.1. Quick Summary
- Same direction → subtract velocities
- Opposite directions → add magnitudes
- Relative velocity can be zero
- It helps us describe motion from different viewpoints