Finding the velocity traveling in a tunnel?

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bobthebuilder1

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Suppose that one has the technology to connect a country in the southern hemisphere with its northern hemisphere antipode by drilling a tunnel straight through the centre of the earth.

A freight train using this tunnel would start free-falling and accelerate towards the centre of the earth.

What would be its velocity at R kilometers away from the centre of the earth?

The gravitational acceleration changes linearly with depth, decreasing from one standard g at the sea level to 0 at the centre of the earth; or a= - g.R/RE where R is the distance from the centre of the earth and RE is the radius of the earth.

R = 3312km

Someone please help me?
 
Hm, so this question seems eerily familiar. Probably because I already answered it when someone else asked.

Here I get the formula:
http://answers.yahoo.com/question/index;_ylt=AswRXJJv8VWzYL8ig6vpR8fsy6IX;_ylv=3?qid=20090929002846AAjt6z0

And here I get the answer for the specific case of R = 3312:
http://answers.yahoo.com/question/index;_ylt=AgddLpwVsuUR8Ul6sIKwbnHty6IX;_ylv=3?qid=20090929021225AARPXIw&show=7#profile-info-aY0DMaZraa

If you don't care about how to get the answer, then it is:
v = 22,800 m/s to three significant figures.

But you should care, so I advise you to read my answers in the above links.
 
here, u know that it changes linearly.
at R, acc. = g * R/Re
at Re, acc. = g
so, on an average, the acc. = g(R/Re +1)/2
Initial Velocity = 0
acc. = g(R/Re + 1)/2
Distance = 3312 km
u can calculate the final velocity

NOTE: my answer may be wrong, maybe the we cannot take the average acc., so if i feel its wrong i'll delete it.
PLEASE INFORM ME, IF I AM WRONG. I'll appreciate it.
 
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