Two parallel rail tracks run north-south. On one track train A moves north with a speed of `54 km h^(-1)` and on the other track train B moves south with a speed of `90 km h^(-1)`. The velocity of train A with respect to train B is

Options

A. `10 m s^(-1)`
B. `15 m s^(-1)`
C. `25 m s^(-1)`
D. `40 m s^(-1)`

Explanation

To find the velocity of train A with respect to train B, we can follow these steps:

### Step 1: Convert the speeds from km/h to m/s
- Train A's speed: \( 54 \, \text{km/h} \)
- Train B's speed: \( 90 \, \text{km/h} \)

To convert km/h to m/s, we use the conversion factor:
\[ 1 \, \text{km/h} = \frac{1000 \, \text{m}}{3600 \, \text{s}} = \frac{1}{3.6} \, \text{m/s} \]

Calculating for both trains:
\[ \text{Speed of Train A} = 54 \times \frac{1}{3.6} = 15 \, \text{m/s} \]
\[ \text{Speed of Train B} = 90 \times \frac{1}{3.6} = 25 \, \text{m/s} \]

### Step 2: Assign directions to the velocities
- Assume north is positive and south is negative.
- Therefore, the velocity of train A (moving north) is:
\[ V_A = +15 \, \text{m/s} \]
- The velocity of train B (moving south) is:
\[ V_B = -25 \, \text{m/s} \]

### Step 3: Calculate the relative velocity of train A with respect to train B
The formula for relative velocity is:
\[ V_{A/B} = V_A - V_B \]

Substituting the values:
\[ V_{A/B} = 15 - (-25) = 15 + 25 = 40 \, \text{m/s} \]

### Final Answer
The velocity of train A with respect to train B is:
\[ \boxed{40 \, \text{m/s}} \]

---