Can you lay $ \aleph_1$ many people on a railway track? Recently an image was posted to this trolley problem meme page.
The image shows two tracks: one with $ \aleph_0 $  many people and another with $ \aleph_1 $ many.

A discussion broke out in the comments as to whether it is possible to even have $ \aleph_1 $  many people on the track. Roughly the two arguments were:
No- You cannot lay uncountably many people in a line.
Yes- If you assume the axiom of choice we can define a well ordering of a set of cardinitality $ \aleph_1 $  and lay people on the track using this ordering.
What is the correct answer?
 A: We'll pretend the track is a copy of $[0, \infty)$.
For infinitely thin people you don't even need a well-ordering. You can just put one person at each real number position along the track. Since $|[0,\infty)| = |\mathbb R| \ge \aleph_1$ you can lay at least that many people along the track.
For people of positive finite width this cannot be achieved. For then every person would lie over at least one rational number. Since no two people occupy the same space that would mean there are at least $\aleph_1$ many rational numbers. But we know this is not true.
Of course there are many other possible railways.
For example the long line which is obtained by arranging $\aleph_1$ many copies of $[0,1)$ end-to-end. Then we could put one person in each copy of $[0,1)$ easy. The problem with this approach is that no finite speed is sufficient for the train to ever reach the end of the track in finite time. In fact the long line starts with a copy of $[0,\infty)$ and there's no reason to believe the train can ever get beyond that. 
Of course there are loads of long railways that are nothing like well-ordered. For example the lexicographically-ordered-square or the product $[0,1) \times [0,\infty)$ with order given by $(a,b) \le (x,y) \iff b \le y$ and $a \le x$. But it's harder to imagine how these would function as railways
since once the train gets past $[0,1) \times \{0\}$ there is already infinitely much track behind it. Formally this is saying the following:

Exercise: Prove every continuous increasing function $[0,\infty) \to [0,1) \times [0,\infty)$ with $0 \mapsto (0,0)$ has range contained in $[0,1) \times \{0\}$.
Hint: $[0,\infty)$ does not admit a family of uncountably many pairwise disjoint open sets.

Conclusion: Don't pull the lever. Any reasonable choice of long railway starts with a copy of the short railway and the train never gets beyond that initial copy. So the train will kill people twice as quickly on the upper line to the lower line. Once we reach the end of time the upper train will fall off the end of the track while the lower train will carry on chugging. But we're not going to be around to worry about that.
Addendum: This assumed the people are packed equally densely on both lines. If they are packed three times denser below for example you should pull the lever.
