As a train approaches the city it sees a stalled car on the tracks. The train slams on its brakes going from 25 m/s to rest in 30 s. How far away was the stalled car when the train conductor slammed on the brakes?

To find the distance between the stalled car and the train when the brakes were applied, we can use the equation of motion:

\[d = v_i \cdot t + \frac{1}{2} \cdot a \cdot t^2\]

Where:
- \(d\) is the distance traveled
- \(v_i\) is the initial velocity
- \(t\) is the time taken
- \(a\) is the acceleration

First, let's calculate the acceleration of the train.

Given:
Initial velocity (\(v_i\)) = 25 m/s
Time taken (\(t\)) = 30 s
Final velocity (\(v_f\)) = 0 m/s (since the train comes to rest)

The acceleration (\(a\)) can be calculated using the equation:

\[a = \frac{v_f - v_i}{t}\]

Plugging in the values:

\[a = \frac{0 - 25}{30} \, \text{m/s}^2\]

Simplifying:

\[a = -\frac{25}{30} \, \text{m/s}^2\]

Now that we have the acceleration, we can calculate the distance (\(d\)) using the equation mentioned earlier.

Since the train is decelerating to a stop, the acceleration will have a negative sign. We take the absolute value of the acceleration to ensure a positive distance.

\[d = v_i \cdot t + \frac{1}{2} \cdot |a| \cdot t^2\]

Plugging in the values:

\[d = 25 \, \text{m/s} \cdot 30 \, \text{s} + \frac{1}{2} \cdot \left|\frac{25}{30} \, \text{m/s}^2\right| \cdot (30 \, \text{s})^2\]

Simplifying:

\[d = 750 \, \text{m} + \frac{1}{2} \cdot \frac{25}{30} \cdot 900 \, \text{m}\]

Calculating the second term:

\[\frac{1}{2} \cdot \frac{25}{30} \cdot 900 \, \text{m} = \frac{25}{4} \cdot 30 \, \text{m}\]

Simplifying:

\[\frac{25}{4} \cdot 30 \, \text{m} = \frac{25}{4} \cdot 30 \, \text{m} = \frac{25}{2} \cdot 15 \, \text{m}\]

Further simplifying:

\[\frac{25}{2} \cdot 15 \, \text{m} = 25 \cdot \frac{15}{2} \, \text{m} = 375 \, \text{m}\]

Now, substituting the value of \(d\):

\[d = 750 \, \text{m} + 375 \, \text{m} = 1125 \, \text{m}\]

Therefore, the stalled car was 1125 meters away from the train when the conductor slammed on the brakes.