Ared train travelling at 72 km/h and a green train travelling at 144 km/h are headed toward each
other along a straight, level track. when they are 950 m apart, each engineer sees the other train
and applies the brakes, which slow each train at the rate of 1.0 m/s2. is there a collision? if yes,
give the speed of the red train and the speed of the green train at impact, respectively. if no, give the
separation between the trains when they stop.

  Collision will occur.

  Speed of red train when they collide = 0 m/s.

  Speed of green train when they collide = 10 m/s.

Explanation:

Speed of red train = 72 km/h = 20 m/s

Speed of green train = 144 km/h = 40 m/s.

Deceleration of trains = 1 m/s²

For red train:-

    Equation of motion v = u + at

              u = 20 m/s

              v = 0 m/s

              a = -1 m/s²

    Substituting

             0 = 20 - 1 x t

             t = 20 s.

    Equation of motion s = ut + 0.5at²

              u = 20 m/s

              t = 20 s

              a = -1 m/s²    

    Substituting

             s = 20 x 20 - 0.5 x 1 x 20² = 200 m

   So red train travel 200 m before coming to stop.

For green train:-

    Equation of motion v = u + at

              u = 40 m/s

              v = 0 m/s

              a = -1 m/s²

    Substituting

             0 = 40 - 1 x t

             t = 40 s.

    Equation of motion s = ut + 0.5at²

              u = 40 m/s

              t = 40 s

              a = -1 m/s²    

    Substituting

             s = 40 x 40 - 0.5 x 1 x 40² = 800 m

   So green train travel 800 m before coming to stop.

 Total distance traveled = 800 + 200 = 1000 m>950 m.

  So both trains collide.

  Distance traveled by green train when red train stops(t=20s)

     Equation of motion s = ut + 0.5at²

              u = 40 m/s

              t = 20 s

              a = -1 m/s²    

    Substituting

             s = 40 x 20 - 0.5 x 1 x 20² = 600 m

    Total distance after 20 s = 600 + 200 = 800 m< 950m . So they collide after red train stops.

  Speed of red train when they collide = 0 m/s.

  Distance traveled by green train when they collide = 950 - 200 = 750 m

  Equation of motion v² = u² + 2as

              u = 40 m/s

              s= 750 m

              a = -1 m/s²    

    Substituting  

              v² = 40² - 2 x 1 x 750 = 100

               v = 10 m/s

  Speed of green train when they collide = 10 m/s.

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