Word Problem?

Question

Two trains, one travelling at 100 km/h and the other at 128 km/h are headed towards one another along a straight level track. When the trains are 1.2 km apart, each engineer simultaneously sees the other's train and applies the brakes. Both trains have equal, constant decelerations of 0.9 m/s^2. Will there be collision?

can i please see the steps involved in solving this problem? Thank uu

Answer 1

The standard equations for motion under constant acceleration is:

Vf = Vi + A x T
D = Vi x T + (1/2) x A x T^2

We can treat each train independently.

For each train we have the initial velocity Vi, the final velocity (which is 0), and the acceleration A, so we can use the velocity equation to compute the time that each train takes to stop.

With the time, we can use the distance equation to compute the the stopping distances.

If the sum of the stopping distances is less than 1.2 km, the trains don't collide.

But if the sum is greater than 1.2 km, there is still one wrinkle. One train is going to stop before the other. What happens if the stopped train starts moving backwards? That might allow it to avoid the collision, but since we aren't told the acceleration in reverse, we can't check for this. possibility.