The driver of a train moving at a speed v1 sights another train at a distance d ahead of him, moving in the same direction with a slower speed v2. He immediately applies brakes to achieve a constant retardation a. There will be no collision if d is greater than(v1−v2)2a(v21−v22)a(v1−v2)22a(v21−v22)2a
Question
The driver of a train moving at a speed v1 sights another train at a distance d ahead of him, moving in the same direction with a slower speed v2. He immediately applies brakes to achieve a constant retardation a. There will be no collision if d is greater than(v1−v2)2a(v21−v22)a(v1−v2)22a(v21−v22)2a
Solution
The given statement seems to be a formula for avoiding collision between two trains moving in the same direction. However, it's not properly formatted which makes it difficult to understand.
Let's break it down:
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The driver of a train moving at a speed v1 sights another train at a distance d ahead of him, moving in the same direction with a slower speed v2.
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He immediately applies brakes to achieve a constant retardation a.
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There will be no collision if the distance d is greater than a certain value.
The formula for this value seems to be given as (v1−v2)²/a or (v1²−v2²)/2a, but it's not clear due to the formatting.
If we assume the formula is (v1−v2)²/2a, it means that the distance d should be greater than the square of the difference in speeds divided by twice the retardation. This would ensure that the first train has enough distance to slow down and stop before reaching the second train.
If the formula is (v1²−v2²)/2a, it means that the distance d should be greater than the difference of the squares of the speeds divided by twice the retardation. This would also ensure that the first train has enough distance to slow down and stop before reaching the second train.
In both cases, the formula is derived from the equations of motion.
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