As two trains move along a track, their conductors suddenly notice that they are

Question

As two trains move along a track, their conductors suddenly notice that they are headed toward each other. The figure below gives their velocities v as functions of time t as the conductors slow the trains. The figures vertical scaling is set by vs = 40.0 m/s. The slowing process begin when the trains are 200 m apart. The distance between both trains when they've stopped is 40 m. What is the velocity of the two trains when they are 80 m apart?

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Explanation / Answer

Distance travel by first train = Area of the upper triangle in the graph

                                        = (1/2) x base x height

                                         = 0.5 x 5 s x 40 m/s (Since height = v s = 40)

                                    S = 100 m

Distance travel by second train = Area of the lower triangle in the graph

                                        = (1/2) x base x height

                                         = 0.5 x 4 s x 30 m/s (Since height = (3/4)v s = (3/4)40 = 30 m/s)

                                   S' = 60 m

Total distance travel by two trains S " = S + S '

                                                      = 100 m + 60 m

                                                      = 160 m

Initial sepration of the two trains = 80 m

Therefore the separation when both trains have stopped = /80 m - S "/

                                                                                 = /80 m - 160 m/

                                                                                 = 80 m

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