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?

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!