#Hole through the earth

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vestal idol
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The exercise is as following:
Calculate the acceleration, force and velocity of an object thrown in a hole through the centre of the Earth, assuming the density of the Earth is homogeneous at points 0, half way between surface and centre, and in the centre. So far I've managed to calculate the force and acceleration, but since the acceleration is dependant on the distance travelled/ to the centre, I haven't found a way to calculate the velocity.

night kestrelBOT
vestal idol
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<@&286206848099549185>

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This is the original exercise in German, I've used a(r) = (GM * r^3)/(r^2 R^3) = g * r / R

vestal idol
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Where can I go if no one can solve this?

vestal idol
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Anyone?

hearty shadow
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you could find a potential energy function and use that to find velocity