A train starts from rest and accelerates for 150s, travels at a constant speed for 300s, and then decelerates to rest for 200s. If the total distance covered is 10450m, find the maximum speed reached

Here's the solution to question 4:

The problem describes a train's journey with three phases:

1. Acceleration from rest for 150 seconds.
2. Constant speed for 300 seconds.
3. Deceleration to rest for 200 seconds.

The total distance travelled is 10450 m. Let $V_{max}$ be the maximum speed attained.

The speed-time graph for this journey is a trapezium. The total distance travelled is the area under this graph.
The area can be broken down into three parts:

• Area 1 (acceleration phase): A triangle with base 150 s and height $V_{max}$.
• Area 2 (constant speed