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Math Help - rate of train decelerating to avoid a crash

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    rate of train decelerating to avoid a crash

    train A which travels 80m/s is 1,500m behind trainB which is traveling at 30m/s in the same direction on the same track.at what rate must train Adecelerate to avoid a crash?

    if anyone could help,
    thanks Ronan.
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  2. #2
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    Quote Originally Posted by ronan116 View Post
    train A which travels 80m/s is 1,500m behind trainB which is traveling at 30m/s in the same direction on the same track.at what rate must train Adecelerate to avoid a crash?

    if anyone could help,
    thanks Ronan.
    The minimum constant deceleration will have train A travelling at 30 m/s when it is at the same position as train B.

    Let the distance travelled by train B at time t_B be x_B. Then

    x_B = 30 t_B .... (1)

    Data for Train A:

    x = (1500 + x_B) m
    u = 80 m/s
    v = 30 m/s
    t = t_B s

    Use the usual formula x = \left( \frac{u + v}{2} \right)t:

    x_B + 1500 = \left( \frac{80 + 30}{2}\right) t \Rightarrow x_B = 55t - 1500 .... (2)

    Solve equations (1) and (2) simultaneously for t_B.

    So for Train A you now have:

    u = 80 m/s
    v = 30 m/s
    t = t_B = ....
    a = ?

    Use an appropriate formula to solve for a.
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