Motion Depends on the Observer
Motion is always read relative to a frame of reference. An object that looks fast to an observer beside the road can look slow, still, or moving in the opposite direction to another observer who is also moving.
If the observed object is named and the observer is named , the velocity of relative to is:
Positive and negative signs still matter because they show direction along the chosen axis.
Relative motion does not create a new motion. It reads the same motion from a different observer's seat.
- Car A
- Car B
- Relative velocity of B to A
- As seen from A
- B appears to move right relative to A.
Velocity Changes When the Observer Moves Too
An object's velocity according to an observer changes when the observer is also moving. We compare not only the observed object, but also the motion of the observer.
Suppose rightward is chosen as positive. A car moves at and a taxi moves at . To a passenger in the taxi, the car appears to move backward:
The negative value means the relative motion points left.
When two vehicles move in the same direction, the faster observer can see the other vehicle as moving backward. That does not mean the car turns around relative to the road. It only means the reading changes from the taxi passenger's seat.
When the Observer Is Still
If the observer is the ground or a stationary platform, relative velocity is the same as velocity relative to the ground.
That is why, in many simple problems, a velocity with no extra frame stated is usually assumed to be relative to the ground.
When Both Are Moving
If two objects move in opposite directions, the magnitude of relative velocity can be greater than each object's velocity relative to the ground. For example, a car moves right at , while a truck moves left at .
To the truck driver, the car's velocity is:
The value means the car appears to approach from the positive direction with a relative speed greater than either vehicle's speed relative to the ground.
Relative motion does not change the actual motion. It changes how the motion is read by different observers.
What the Observer Sees Is the Difference
| Situation | Calculation | Meaning of the relative motion |
|---|---|---|
| Observer is still | ||
| Observer is faster in the same direction | The object appears to move in the negative direction | |
| Observer moves in the opposite direction | The object appears to move in the positive direction |
So, before saying an object is fast, slow, still, or moving backward, always check the frame of reference.
