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Deceleration of Train to Avoid Collision

  1. Sep 15, 2014 #1
    1. The problem statement, all variables and given/known data


    The engineer of a passenger train traveling at 25.0 m/s sights a freight train whose caboose is 200 m ahead on the same track. The freight train is traveling at 15.0 m/s in the same direction as the passenger train. The engineer of the passenger train immediately applies the brakes, causing a constant acceleration of 0.100 m/s^2, while the freight train continues with constant speed. Take x=0 at the location of the front of the passenger train when the engineer applies the brakes. Find the deceleration of the passenger needed in order to avoid collision.


    2. Relevant equations


    Vx^2=Vox^2 + 2ax(x-xo)

    3. The attempt at a solution

    I'm using V of the freight train as the final and the V of the passenger as the initial and 200m as the distance.
    Rearranging the equation,
    (15^2-25^2)/(200*2)=-1m/s^2

    Or do I use the relative velocity between passenger train and freight train 10m/s (25-15) as the initial and 0m/s (coming to a complete stop) as the final.
    (0^2-10^2)/(200*2)=-0.25m/s^2
     
  2. jcsd
  3. Sep 15, 2014 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    The first one cannot be true as the passenger train has more than 200m to slow down. It is possible to fix it, but using the second approach is much easier.
     
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