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Commuter train

  1. Nov 9, 2004 #1
    A commuter train can minimize the time t between two stations by accelerating (a1 = .20 m/s^2) for a time t1, then undergoing a negative acceleration (a2 = -.5 m/s^2) by using his brakes for a time t2. Since the stations are .90 km apart, the train never reaches its maximum velocity. Find the total travel time, t.

    My method:

    deltaS= (Vf^2-Vo^2)/2a
    900= (Vf^2/.4) + (Vf^2)
    900= 2.5Vf^2 + Vf^2
    Vf= 16 m/s

    and then I used: Vf = Vo + at
    16= .2t
    t=80 s

    0= 16 - .5t
    t=32 s

    total t= 112 seconds

    Can anyone please confirm this?
  2. jcsd
  3. Nov 9, 2004 #2

    Doc Al

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    Staff: Mentor

    900 m is the entire distance. Note that the initial and final speeds are both zero over the 900 m.

    Break the motion into two pieces, each with a different acceleration. Use that same kinematic formula, but for each piece separately. (The first piece goes from v = 0 to v = V1; the second goes from v = V1 to v = 0.)
  4. Nov 9, 2004 #3
    I think that's what I did. Is my answer incorrect? I'm pretty sure my method is what you explained. If I'm wrong, please let me know. The Vf is the same as V1
  5. Nov 9, 2004 #4

    Doc Al

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    Staff: Mentor

    Looks good. (I missed what you did, at first look.)
  6. Nov 9, 2004 #5
    Ohh, thanks for the confirmation. I'm really happy I know what I'm doing :approve:
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