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21 November, 00:03

A 180 meter long train, travelling at a constant speed, is passing a car driving on an adjacent lane at a speed of 72 km/h. Knowing that the overshoot lasted 60 seconds, what is the speed of the train in km/h?

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  1. 21 November, 00:38
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    The velocity of the train is 82.8 km/h

    Explanation:

    The equation for the position of the train and the car is as follows:

    x = x0 + v · t

    Where:

    x = position at time "t".

    x0 = initial position.

    v = velocity.

    t = time.

    First, let's calculate the distance traveled by the car in 60 s (1/60 h). Let's place the origin of the frame of reference at the front of the train when it starts to pass the car so that the initial position of the car is 0 (x0 = 0 m):

    x = 0 m + 72 km/h · (1/60) h

    x = 1.2 km.

    Then, if the whole train passes the car at that time, the position of the front of the train at that time will be 1.2 km + 0.18 km = 1.38 km.

    Then using the equation of position we can obtain the velocity:

    x = x0 + v · t

    1.38 km = 0 m + v · (1/60) h

    1.38 km / (1/60) h = v

    v = 82.8 km/h

    The velocity of the train is 82,8 km/h

    The same result could be obtained using the rear of the train. You only have to identify where the rear is at t = 0 and where it is at t = 60 s.

    Try it!
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