please help with applied maths question

electriks

(ex 2C Q23 in fundamental applied mathematics)

A train is travelling at 80m/s. A train 1500m ahead is travelling at 30m/s. What is the minimum deceleration for train 1 to avoid a crash.

Please help if you know how to work it out.

MathsManiac

Here are two possible ways to approach it:

First way:
Find an expression in t for s1, the distance travelled after t seconds by the train in front, which is moving at constant velocity.
Taking a as the deceleration of the train behind, find an expression in t and a for s2, the distance it has travelled after t seconds..
If s2 - s1 reaches 1500 the trains will crash, so the question is basically: for what values of a does the equation s2 - s1 = 1500 have no solutions for t?

Second way (easier, provided you can visualise "relative motion"):
Consider the situation as it appears to an observer standing on the train in front. Relative to such an observer, a train is approaching from behind at a net speed of 50 m/s and is 1500 metres away. That train must "stop" before it reaches him. So, the question is equivalent to:
What's the minimum deceleration that you must apply to a train tranelling at 50 m/s in order that it will stop in less than 1500 metres?

Hope this helps.

(By the way, I assumed the trains were travelling in the same rather than opposite directions!)

electriks

cheers!! never even considered doing it the 2nd way:)
thanks v. much