A train 350 m long is moving on a straight track with a speed of 84.1 km/h. The engineer applies the brakes at a crossing, and later the last car passes the crossing with a speed of 15.8 km/h. Assuming constant acceleration, determine how long the train blocked the crossing. Disregard the width of the crossing.

t = 25.0 s

Explanation:

Assuming that the engineer applies the brakes just over the crossing, the train moves exactly 350 m at a constant acceleration, with a final speed (when the last car of the train leaves the crossing) of 15.8km/h.Since we know the initial and final speeds, and the horizontal distance traveled (the length of the train) we can use the following kinematic equation to get the acceleration:

       

Since we need to find the time in seconds, it is advisable to convert vf and  vo to m/s first, as follows:

       

     

Replacing (2) and (3) in (1), since Δx =350m, we can solving for a:

       

In order to get the time, we can simply use the definition of acceleration, and rearrange terms: