Physics

A train travels 30m/s then breaks are suddenly applied producing a retarding force equal to 1/10 of the weight of the train runs on the distance through which the train runs on the track before coming to rest in.

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  1. F = - mg/10 = m a
    so
    a = -g/10

    v = Vi + at = 30 - g t /10
    at stop v = 0
    t = 300/g = time to stop

    d = Vi t + (1/2)a t^2
    = 30(300/g) -(1/2)(g/10)(300^2/g^2)
    = 9000/g - (1/2)(9000/g)
    = 4500/g
    about 450 meters

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  2. alternate way using energy
    (1/2) m Vi^2 = F d
    F = mg/10
    (1/2) m Vi^2 = m g d/10
    (30)^2 = g d/5
    900 *5 /g = d
    d = 4500/g

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