As two trains move along a track their conductors suddenly n

As two trains move along a track, their conductors suddenly notice that they are headed toward each other. The figure gives their velocities v as functions of time t as the conductors slow the trains. The figure\'s vertical scaling is set by vs = 48.0 m/s. The slowing processes begin when the trains are 200 m apart. What is their separation when both trains have stopped?

Solution

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 48 m/s      Since height = v _s = 48

                                    S = 120 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 36 m/s      Since height = (3/4)v _s = (3/4)48 = 36 m/s

                                   S\' = 72 m

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

                                                      = 120 m + 72 m

                                                      = 192 m

Initial sepration of the two trains = 200 m

Therefore the separation when both trains have stopped = 200 m - S \"

                                                                                 = 200 m - 192 m

                                                                                 = 8 m