**Answer:**

To find the distance the train will go before it is brought to rest, we need to use the equation of motion:

v^2 = u^2 + 2as

Where:
v = final velocity (0 m/s, as the train is brought to rest)
u = initial velocity (90 km/h = 25 m/s)
a = acceleration (-50 m/s^2, negative sign indicates deceleration)
s = distance

**Initial Velocity (u):**
Given that the initial velocity of the train is 90 km/h, we need to convert it to m/s:
90 km/h = 90 * (1000 m / 1 km) * (1 h / 3600 s) = 25 m/s

**Acceleration (a):**
The brakes are applied to produce a uniform acceleration of -50 m/s^2. The negative sign indicates that the train is decelerating.

**Final Velocity (v):**
The final velocity of the train is 0 m/s, as it is brought to rest.

**Distance (s):**
We can rearrange the equation of motion to solve for distance (s):

s = (v^2 - u^2) / (2a)

Substituting the given values:

s = (0^2 - 25^2) / (2 * -50)
s = (-625) / (-100)
s = 6.25 m

Therefore, the train will go a distance of 6.25 meters before it is brought to rest.

**Explanation:**
When the brakes are applied to the train, a negative acceleration is produced. This negative acceleration acts in the opposite direction to the motion of the train, causing it to slow down and eventually come to a stop.

The equation of motion helps us calculate the distance the train will travel before coming to rest. By substituting the initial velocity, final velocity, and acceleration into the equation, we can solve for distance.

In this case, the train's initial velocity is 25 m/s, and the brakes produce a negative acceleration of -50 m/s^2. The final velocity is 0 m/s, as the train comes to rest. By plugging these values into the equation, we find that the train will travel a distance of 6.25 meters before it stops completely.

It's important to note that the negative sign in the acceleration indicates deceleration or slowing down. If the acceleration were positive, it would indicate an increase in speed.