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Thread: 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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    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 $\displaystyle t_B$ be $\displaystyle x_B$. Then

    $\displaystyle x_B = 30 t_B$ .... (1)

    Data for Train A:

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

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

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

    Solve equations (1) and (2) simultaneously for $\displaystyle t_B$.

    So for Train A you now have:

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

    Use an appropriate formula to solve for a.
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