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 a function of time t as the conductors slow the trains. The figure's vertical scaling is set by vs = 29.0 m/s. The slowing processes begin when the trains are 191 m apart. What is their when both trains have stopped?
To find the time when both trains have stopped, we need to determine the time at which the velocities of both trains become zero.
Looking at the graph, we can see that the train on the left has a decreasing velocity until it reaches zero, and the train on the right has an increasing velocity until it reaches zero.
To find the time when the train on the left stops, we need to find the x-intercept of the left line (the decreasing line). From the graph, we can see that the left line crosses the x-axis (velocity = 0) at about t = 19 seconds.
To find the time when the train on the right stops, we need to find the x-intercept of the right line (the increasing line). From the graph, we can see that the right line crosses the x-axis (velocity = 0) at about t = 9 seconds.
So, the train on the left stops at t = 19 seconds and the train on the right stops at t = 9 seconds.
To find their separation at these times, we can use the equation: separation = initial separation + velocity * time.
Given that the initial separation is 191 m, and both trains have stopped at their respective times, the separation when both trains have stopped is:
separation = 191 m + (0 m/s) * (9 seconds) = 191 m
Therefore, when both trains have stopped, their separation is 191 m.