**Given:**
- The train starts from rest and accelerates uniformly for 100s.
- It runs at a constant speed for 5 minutes (300s).
- It then comes to a stop with uniform retardation in the next 150s.
- The total distance covered by the train is 4.25 km.

**To find:**
i) The constant speed of the train.
ii) The acceleration of the train.
iii) The retardation of the train.

**Solution:**

Let's solve each part of the problem step by step.

**i) Finding the constant speed:**

To find the constant speed, we need to calculate the distance covered during the constant speed phase.

Total distance covered = Distance covered during acceleration + Distance covered during constant speed + Distance covered during retardation

Given:
Distance covered during acceleration = 0.5 * acceleration * time^2 (since the train starts from rest and accelerates uniformly)
Distance covered during constant speed = constant speed * time
Distance covered during retardation = 0.5 * retardation * time^2 (since the train comes to a stop with uniform retardation)

Substituting the given values:
4.25 km = 0.5 * acceleration * (100s)^2 + constant speed * (300s) + 0.5 * retardation * (150s)^2

Simplifying the equation, we get:
4.25 km = 0.5 * acceleration * 10000s^2 + constant speed * 300s + 0.5 * retardation * 22500s^2

Now, we know that the train runs at a constant speed during the 5-minute phase. Therefore, the distance covered during this phase is equal to the product of the constant speed and the time.

Substituting the given distance and time values, and rearranging the equation, we get:
4.25 km - 0.5 * acceleration * 10000s^2 - 0.5 * retardation * 22500s^2 = constant speed * 300s

Simplifying further, we get:
constant speed = (4.25 km - 0.5 * acceleration * 10000s^2 - 0.5 * retardation * 22500s^2) / (300s)

So, by substituting the values of acceleration and retardation, we can find the constant speed of the train.

**ii) Finding the acceleration:**

To find the acceleration, we can use the equation:
Distance covered during acceleration = 0.5 * acceleration * time^2

Given:
Distance covered during acceleration = 4.25 km - Distance covered during constant speed - Distance covered during retardation
Time = 100s

Substituting the given values, we get:
4.25 km - constant speed * 300s - 0.5 * retardation * 22500s^2 = 0.5 * acceleration * (100s)^2

Simplifying the equation, we get:
4.25 km - constant speed * 300s - 0.5 * retardation * 22500s^2 = 0.5 * acceleration * 10000s^2

Rearranging the equation, we get:
acceleration = (4.25 km - constant speed * 300s - 0.5