What the Result Means
Relative motion answers a simple but powerful question: how fast does object A appear to move when viewed from object B? The answer depends on the reference frame.
The calculator reports both the relative velocity where direction matters and the relative speed, which is only the magnitude.
Three Cases This Page Handles
| Case | Use it when | Core equation |
|---|---|---|
| Same direction | Two cars, trains, or objects move along the same line. | |vA − vB| |
| Opposite directions | Two objects move toward each other or away from each other along one line. | |vA + vB| |
| 2D vector motion | You know x and y velocity components. | |vA − vB| |
| Rotational motion | You have angular velocity and radius. | vt = ωr |
Relative Speed vs Relative Velocity
Relative velocity keeps direction. It can be positive, negative, or a vector. Relative speed is the size of that velocity, so it is normally reported as a non-negative number.
Rotational Motion Mistake to Avoid
In rotational problems, angular velocity is not the same as linear speed. First calculate the tangential speed:
If there is also radial motion, combine the radial and tangential components with the Pythagorean relationship:
Practical Examples
- Traffic: closing speed between two vehicles.
- Robotics: velocity of an end effector relative to a moving base.
- Rotating machinery: tangential speed at the rim of a wheel or shaft.
- Sports physics: ball speed relative to a moving player.
- Aerospace: airspeed and wind are relative-motion problems.
Common Mistakes
- Adding speeds when the objects actually move in the same direction.
- Subtracting speeds when the objects move toward each other.
- Forgetting that velocity has direction.
- Using rpm directly as linear speed instead of converting to angular velocity first.
- Mixing m/s, km/h, mph, and ft/s without conversion.
Frequently Asked Questions
What is relative speed?
Relative speed is how fast one object appears to move compared with another object.
Is relative velocity always positive?
No. Relative velocity can be positive or negative in one-dimensional motion. Relative speed is the magnitude, so it is non-negative.
When do relative speeds add?
They add when two objects move in opposite directions along the same line, such as two vehicles approaching each other.
When do relative speeds subtract?
They subtract when two objects move in the same direction along the same line.