A passenger train and a freight train are on a collision course on a straight st

Question

A passenger train and a freight train are on a collision course on a straight stretch of track. At t = 0, the trains are 3.000 km apart and both trains simultaneously apply their brakes. In a particular 1D coordinate system the passenger train's initial position is -2.500 km and the freight train is at +0.500 km. The velocity versus time graphs (not to scale!) until each comes to rest below are shown below. (Note: You first need to reason which 'line' corresponds to which train.) On the graph v1,0 = 39.5 m/s, t1 = 41.6 s, v20 = -40.2 m/s and t2 = 69.2 s.

How far apart (in meters) are the trains when they both come to rest?

Note: Nobody was injured in the making of this question.

Explanation / Answer

The image is not visible. however it is still possible to answer the question from the data given.

The v-t curve for passenger would start at (0,39.5) and end at (41.6,0), have negative slope and lie in the first quadrant.

The v-t curve for Freight would start at (0,-40.2) and end at (69.2,0), have positive slope and lie in the fourth quadrant.

Displacement is given by area under v-t curve.

Displacement of Passenger = 0.5*39.5*41.6 = 821.6m

Displacement of Freight = 0.5*(-40.2)*(69.2 = -1390.92m

Final Position of Passenger = -2500 + 821.6 = -1678.4m

Final position of Freight = 500 - 1390.92 = -890.92m

Separation between trains = -890.92 - (-1678.4) = 787.48 m

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