The driver of a train travelling at 115 km/hour sees on the same track 100 m in front of him a slow train travelling in same direction at 25 km/hr. The least retardation that must be applied to the faster train to avoid a collision will be-

Options

A. ` 3.125 m//s^(2)`
B. `31.25 m//s^(2)`
C. `312.5 m//s^(2)`
D. `0.3125 m//s^(2)`

Explanation

To solve the problem of determining the least retardation that must be applied to the faster train to avoid a collision with the slower train, we can follow these steps:

### Step-by-Step Solution

1. **Convert Speeds from km/h to m/s**:
- The speed of the faster train (Train A) is 115 km/h.
- The speed of the slower train (Train B) is 25 km/h.
- To convert km/h to m/s, we use the conversion factor: \( \text{Speed in m/s} = \text{Speed in km/h} \times \frac{5}{18} \).
...