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Two trains are heading toward each other on the same track with velocities v1 and v2 respectively. The drivers,noticing this when the trains are at distance x apart, apply brakes, giving same acceleration y to each train. The necessary condition for collision is?

  • physics -

    [v1*t -(a/2)t^2] + [v2*t - (a/2)t^2] = x

    (v1 +v2)*t - a t^2 = x

    a is the acceleration rate.

    The time t to collision depends upon the deceleration rate a as well as v1+v2 and x.

    If there is no real solution to the quadratic, they do not collide.

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