What is the physics involved in moving the train at the highest speed to get across the unstable railroad bridge.

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The law you are looking for here is Newton's third law, for every action there is an equal and opposite reaction. The higher the speed of the train, the less pressure it exerts at any one portion of the unstable bridge. Therefore, the bridge is less likely to collapse.

**Sources:**

in this book it is that hopefully if they go fast they will reach the other side before the bridge colapses

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