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Two trains, moving at velocities u(1) an...

Two trains, moving at velocities `u_(1)` and `u_(2)` travel along the same line towards each other. Drivers of both the trains when the trains are at a distance x apart simultaneously apply brakes producing retardations `a_(1)` and `a_(2)` , respectively. Prove that a collision can be avoided only if `u_(1)^(2)a_(2)+u_(2)^(2)a_(1)=2a_(1)a_(2)x.`

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