A train starts from rest and accelerates uniformly at a rate of 2 m `s^(-2)` for 10 s. It then maintains a constant speed for 200 s. The brakes are then applied and the train is uniformly retarded and comes to rest in 50 s. Find : (i) the maximum velocity reached, (ii) the retardation in the last 50 S, (iii) the total distance travelled, and (iv) the average velocity of the train.

Explanation

To solve the problem step by step, we will break it down into parts as outlined in the question.

### Given Data:
- Initial velocity (u) = 0 m/s (the train starts from rest)
- Acceleration (a) = 2 m/s²
- Time of acceleration (t₁) = 10 s
- Constant speed duration (t₂) = 200 s
- Time of retardation (t₃) = 50 s
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