Two trains are accidentally put on the same track so that they are on a head-on collision course. Train-A is moving at 28 m/s and can decelerate at -4 m/s2. Train-B is moving at 30 m/s and can decelerate at -5 m/s2. When the trains are 190 meters apart they spot each other and immediately apply their brakes. Do they collide?

To determine whether the two trains collide, we need to calculate the distance each train will travel before coming to a complete stop and compare that to the distance between them (190 meters).

### Given:
- Train-A:
  - Initial velocity \( v_{A} = 28 \, \text{m/s} \)
  - Deceleration \( a_{A} = -4 \, \text{m/s}^2 \)

- Train-B:
  - Initial velocity \( v_{B} = 30 \, \text{m/s} \)
  - Deceleration \( a_{B} = -5 \, \text{m/s}^2 \)

- Distance between the trains when they start braking \( d = 190 \, \text{meters} \)

### Steps to solve:
1. **Calculate the stopping distance for each train using the equation:**

\[
d = \frac{v^2}{2a}
\]

Where:
- \( v \) is the initial velocity,
- \( a \) is the magnitude of the deceleration.

2. **Compare the sum of the stopping distances to the initial distance between the trains (190 meters).**

#### 1. Stopping distance for Train-A:
\[
d_{A} = \frac{v_{A}^2}{2 |a_{A}|} = \frac{28^2}{2 \times 4} = \frac{784}{8} = 98 \, \text{meters}
\]

#### 2. Stopping distance for Train-B:
\[
d_{B} = \frac{v_{B}^2}{2 |a_{B}|} = \frac{30^2}{2 \times 5} = \frac{900}{10} = 90 \, \text{meters}
\]

#### 3. Total stopping distance:
\[
d_{A} + d_{B} = 98 + 90 = 188 \, \text{meters}
\]

Since the total stopping distance (188 meters) is less than the distance between the trains (190 meters), **the trains do not collide**. They will stop 2 meters apart.

Would you like to go over the calculations in more detail or have any questions?

Here are five related questions for further exploration:
1. What would happen if Train-A had a slower deceleration?
2. How does increasing the distance between the trains affect the outcome?
3. What if both trains had the same initial velocity?
4. How would a headwind affecting one train impact the scenario?
5. What would happen if the brakes applied with a delay?

**Tip:** Always double-check initial conditions and unit consistency when solving physics problems to avoid mistakes.

Explore the solution to a physics problem involving two trains on a head-on collision course. Calculate stopping distances, analyze deceleration rates, and determine if the trains collide. Suitable for high school physics students.

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