Relative Motion Formula Calculator

\[ v_{AB} = v_A - v_B \]

1. What is the Relative Motion Formula Calculator?

Definition: This calculator computes the relative velocity (\(v_{AB}\)) between two objects A and B, defined as the difference between their velocities using the formula \(v_{AB} = v_A - v_B\).

Purpose: It is used in physics to determine how fast one object is moving relative to another, applicable in scenarios like vehicle motion, navigation, and collision analysis.

2. How Does the Calculator Work?

The calculator uses the relative motion formula:

Formula: \[ v_{AB} = v_A - v_B \] where:

\(v_{AB}\): Relative velocity (m/s, km/s, ft/s, mph)
\(v_A\): Velocity of object A (m/s, km/s, ft/s, mph)
\(v_B\): Velocity of object B (m/s, km/s, ft/s, mph)

Unit Conversions:

Input Velocities (\(v_A\), \(v_B\)):
- 1 m/s = 1 m/s
- 1 km/s = 1000 m/s
- 1 ft/s = 0.3048 m/s
- 1 mph = 0.44704 m/s
Relative Velocity (Output):
- 1 m/s = 1 m/s
- 1 km/s = 1000 m/s
- 1 ft/s = 0.3048 m/s
- 1 mph = 0.44704 m/s

The relative velocity is calculated in m/s and can be converted to the selected output unit (m/s, km/s, ft/s, mph).

Steps:

Enter the velocities of objects A (\(v_A\)) and B (\(v_B\)) with their unit (default: \(v_A = 50 \, \text{m/s}\), \(v_B = 30 \, \text{m/s}\)).
Convert inputs to SI units (m/s).
Calculate the relative velocity in m/s using the formula.
Convert the relative velocity to the selected output unit.
Display the result, rounded to 4 decimal places.

3. Importance of Relative Motion Calculation

Calculating relative velocity is crucial for:

Physics: Analyzing the motion of objects from different reference frames, such as cars on a highway or boats on a river.
Engineering: Designing navigation systems, collision avoidance mechanisms, and traffic flow models.
Education: Teaching the concept of relative motion and vector subtraction in kinematics.

4. Using the Calculator

Examples:

Example 1: Calculate the relative velocity for \(v_A = 50 \, \text{m/s}\), \(v_B = 30 \, \text{m/s}\), output in m/s:
- Enter \(v_A = 50 \, \text{m/s}\), \(v_B = 30 \, \text{m/s}\).
- Relative velocity: \(v_{AB} = 50 - 30 = 20 \, \text{m/s}\).
- Output unit: m/s (no conversion needed).
- Result: \( \text{Relative Velocity} = 20.0000 \, \text{m/s} \).
Example 2: Calculate the relative velocity for \(v_A = 60 \, \text{mph}\), \(v_B = 40 \, \text{mph}\), output in ft/s:
- Enter \(v_A = 60 \, \text{mph}\), \(v_B = 40 \, \text{mph}\).
- Convert to SI: \(v_A = 60 \times 0.44704 = 26.8224 \, \text{m/s}\), \(v_B = 40 \times 0.44704 = 17.8816 \, \text{m/s}\).
- Relative velocity in m/s: \(v_{AB} = 26.8224 - 17.8816 = 8.9408 \, \text{m/s}\).
- Convert to output unit (ft/s): \(8.9408 \times \frac{1}{0.3048} \approx 29.3333 \, \text{ft/s}\).
- Result: \( \text{Relative Velocity} = 29.3333 \, \text{ft/s} \).

5. Frequently Asked Questions (FAQ)

Q: What is relative velocity?
A: Relative velocity is the velocity of one object as observed from the reference frame of another object, calculated as the difference between their velocities.

Q: What does a negative relative velocity mean?
A: A negative relative velocity indicates that object A is moving slower than object B in the chosen positive direction, or moving in the opposite direction.

Q: Can the velocities be in different directions?
A: Yes, the velocities can be positive or negative, representing direction. The calculator assumes a one-dimensional motion along a straight line.