Step 1: Understanding the Concept:
Relative velocity is the velocity of an object as observed from another moving frame of reference.
In one-dimensional motion, if two objects are moving along the same line, their relative velocity is the algebraic difference of their individual velocities relative to the ground.
Step 2: Key Formula or Approach:
Let \( v_A \) be the velocity of car A and \( v_B \) be the velocity of car B.
The velocity of car B with respect to car A is:
\[ \vec{v}_{BA} = \vec{v}_B - \vec{v}_A \]
Sign Convention:
- If both move in the same direction, magnitudes subtract: \( |v_B - v_A| \).
- If they move in opposite directions, magnitudes add: \( |v_B + v_A| \).
Step 3: Detailed Explanation:
1. Identify the given magnitudes and direction:
- Velocity of Car 1 (\( v_1 \)) = 20 m/s.
- Velocity of Car 2 (\( v_2 \)) = 30 m/s.
- Direction: Same direction.
2. Calculate the relative velocity magnitude:
\[ v_{rel} = |v_2 - v_1| = |30 - 20| = 10 \text{ m/s} \]
3. Interpretation:
An observer sitting in Car 1 (moving at 20 m/s) would see Car 2 pull away from them at a speed of 10 m/s.
Similarly, an observer in Car 2 would see Car 1 receding behind them at 10 m/s.
Step 4: Final Answer:
The magnitude of the relative velocity is 10 m/s.
This matches Option (B).