Trains Crossing Platform and Static Objects A train travels at a constant speed, but when it approaches a platform, its path changes, and it must cross it to...
A train travels at a constant speed, but when it approaches a platform, its path changes, and it must cross it to reach its destination. This raises an interesting question: how can the train maintain its speed and avoid colliding with the platform?
Key concepts:
Relative velocity: The relative velocity between the train and the platform tells us the direction in which the train needs to move to avoid collision.
Static objects: Static objects, such as the platform, are objects that do not move and have constant position.
Collisions: Collisions occur when two objects move towards each other at the same speed.
Key equations:
Relative velocity: Relative velocity = Speed of train – Speed of platform
Collisions: Scm = (vi² - vf²)²
Scm is the collision distance
vi is the initial speed of the train
vf is the final speed of the train after crossing the platform
Examples:
Solution:
Relative velocity: 40 m/s - 0 m/s = 40 m/s
Collision distance: Scm = (40 m/s)² - (0 m/s)² = 160 m
Example 2: A train travels at 20 m/s towards a platform that is 10 m long. What is the collision distance and the final speed of the train?
Solution:
Relative velocity: 20 m/s - 0 m/s = 20 m/s
Collision distance: Scm = (20 m/s)² - (0 m/s)² = 40 m
Final speed: vf = 20 m/s - 10 m/s = 10 m/s
Conclusion:
The train maintains its speed by crossing the platform with a specific distance (collision distance) at a constant relative velocity. This ensures a safe passage without colliding with the platform