Two Trains on a railway track

[potterfan3]

Two trains are travelling on the same railway track, which is 1 dimensional and long. Train one is at a position x=-5km and train 2 is at x=10km. Train two is travelling at a velocity of 90m/s, whilst train one is travelling -100m/s. If, at these positions and velocities, the trains were to brake and experience a deceleration of magnitude 20m/s/s, would they crash?

You may assume that there is nothing else causing deceleration

[jomifl]

F30 as this is a hypothetical railway line, I was thinking of the one that goes to the station at the end of the universe.

[Johnysid]

The way you have worded the question, with train one going backwards at 100 m/s and train two going forwards at 90 m/s the trains would never meet. No need for a calculation, they are going in opposite directions.

The trains stop well within the kilometres of separation between them so I would suspect a trick question.

Newton's first equation of motion: v = u + at
Second equation: s = ut + 1/2 at^2
Third: v^2 = u^2 + 2as

Using third equation to calculate distance to stop:
Train travelling at -100 m/s 0 = 10000 + 40 x s so s is - 250m
Train travelling at 90 m/s 0 = 8100 - 40 x s so s is 225 m

(Acceleration and deceleration are directional (vector quantities) so deceleration can have a negative sign as above).

If I were answering the question I would draw a quick graph showing the directions of travel and put in the quick calculation above to show that you have understood the maths and physics even if I had made a mistake taking down the question.

[DTCwordfan]

What nationality was the Big Fat (not allowed to say that now) Controller?

[factor-fiction]

It's a while since I've done this ort of maths but I'm not sure the use of a minus sign makes it a trick question. Isn't velocity also a vector so that can be positive or negative depending on the direction of travel. Train 1 could be travelling East at 90m/s; train 2 could be heading West (towards it) at 100m/s and shown as minus

[DTCwordfan]

Answer: he was Algebraic.

[factor-fiction]

I've just reread the question and maybe I agree with Johnysid about the directions given that the starting point of train 1 is shown as negative and it's velocity is shown as negative so on an xy plane it's moving left, while train 2 is travelling right