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Constant Accerlation problem

  1. Nov 23, 2007 #1
    [SOLVED]Constant Acceleration problem

    1. The problem statement, all variables and given/known data
    When a high speed train traveling at 161 km/hr rounds a bend,he is shocked to see that a locomotive has improperly entered onto the track at a distance D=676 m ahead. The locomotive is moving at 29.0 km/hr away from the train. The engineer of the train immediately applies the brakes. What must be the magnitude of the resulting deceleration if a collision is just to be avoided?

    2. Relevant equations
    v= vi+a*t

    3. The attempt at a solution

    First i convert the speed of the train and the locomotive to m/s:
    train: 44.7 m/s
    Loco: .806 m/s

    Next I make a system of eq. for x
    x= (0)+(44.7)*t+.5*a*t^2 [kinematic equation]
    x= (676) + .806*t {Ini. spacing add the distance trav. by Loc}

    Now I combine the two
    676= 43.9*t+.5*a*t^2

    next I solve for a with respect to t
    0 = 44.7+a*t [kinematic equation]
    a = -44.7/t

    and substitute and solve for t
    676= 43.9*t - .5*(44.7*t)
    t= 31.3

    now I solve for a
    a= -44.7/(31.3) [kinematic]
    a= -1.42 m/sec^2 ANSWER

    However the book gives something different (.994 m/sec^2), I think I'm screwing up in determining the time. Can someone help me in determining my error. Thanks in advance

    edit: to make it less confusing
    Last edited: Nov 23, 2007
  2. jcsd
  3. Nov 23, 2007 #2

    Doc Al

    User Avatar

    Staff: Mentor

    That last one should be: 8.06 m/s.
  4. Nov 23, 2007 #3
    AH I see. Thanks for the proofread, now I know to double check the math as well as the concept too!
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