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22 May, 16:23

A red train travelling at 72 km/h and a green train travelling at 144 km/h are headed toward each

other along a straight, level track. When they are 950 m apart, each engineer sees the other train

and applies the brakes, which slow each train at the rate of 1.0 m/s2. Is there a collision? If yes,

give the speed of the red train and the speed of the green train at impact, respectively. If no, give the

separation between the trains when they stop.

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  1. 22 May, 16:29
    0
    Collision will occur.

    Speed of red train when they collide = 0 m/s.

    Speed of green train when they collide = 10 m/s.

    Explanation:

    Speed of red train = 72 km/h = 20 m/s

    Speed of green train = 144 km/h = 40 m/s.

    Deceleration of trains = 1 m/s²

    For red train:-

    Equation of motion v = u + at

    u = 20 m/s

    v = 0 m/s

    a = - 1 m/s²

    Substituting

    0 = 20 - 1 x t

    t = 20 s.

    Equation of motion s = ut + 0.5at²

    u = 20 m/s

    t = 20 s

    a = - 1 m/s²

    Substituting

    s = 20 x 20 - 0.5 x 1 x 20² = 200 m

    So red train travel 200 m before coming to stop.

    For green train:-

    Equation of motion v = u + at

    u = 40 m/s

    v = 0 m/s

    a = - 1 m/s²

    Substituting

    0 = 40 - 1 x t

    t = 40 s.

    Equation of motion s = ut + 0.5at²

    u = 40 m/s

    t = 40 s

    a = - 1 m/s²

    Substituting

    s = 40 x 40 - 0.5 x 1 x 40² = 800 m

    So green train travel 800 m before coming to stop.

    Total distance traveled = 800 + 200 = 1000 m>950 m.

    So both trains collide.

    Distance traveled by green train when red train stops (t=20s)

    Equation of motion s = ut + 0.5at²

    u = 40 m/s

    t = 20 s

    a = - 1 m/s²

    Substituting

    s = 40 x 20 - 0.5 x 1 x 20² = 600 m

    Total distance after 20 s = 600 + 200 = 800 m< 950m. So they collide after red train stops.

    Speed of red train when they collide = 0 m/s.

    Distance traveled by green train when they collide = 950 - 200 = 750 m

    Equation of motion v² = u² + 2as

    u = 40 m/s

    s = 750 m

    a = - 1 m/s²

    Substituting

    v² = 40² - 2 x 1 x 750 = 100

    v = 10 m/s

    Speed of green train when they collide = 10 m/s.
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