Question

Two trains are moving at 30 m/s in opposite directions on the same track. The engineers see simultaneously that they are on a collision course and apply the brakes when they are 1000 m apart. Assuming both trains have the same acceleration, what must this acceleration be if the trains are to stop just short of colliding?

a) 0.1 m/s²
b) 0.2 m/s²
c) 0.3 m/s²
d) 0.4 m/s²

Answer 1

Using the kinematic equation with given conditions, the necessary deceleration for each train to avoid a collision is found to be 0.9 m/s^2, which doesn't match the provided options.

Step-by-step explanation:

To determine the necessary acceleration for each train to stop before colliding, we can use the kinematic equation vf^2 = vi^2 + 2ad, where vf is the final velocity, vi is the initial velocity, a is the acceleration, and d is the distance. Since each train has to stop, the final velocity vf is 0 m/s, the initial velocity vi is 30 m/s, and the distance d for each train is half the total distance apart, so 1000 m / 2 = 500 m. Plugging these values into the equation gives us 0 = (30 m/s)^2 + 2a(500 m), which simplifies to -900 m^2/s^2 = 1000a. Solving for a gives us an acceleration of -0.9 m/s^2. Since we usually express acceleration as a positive value when talking about slowing down, the necessary deceleration is 0.9 m/s^2. However, this value is not an option in the multiple choices provided, so it's necessary to check if there's an error in the interpretation of the question or the options given.