I wasn't sure about all of them, but my boyfriend is a native speaker, so I just went ahead and asked him.
Here's what he said:
What time do you usually arrive AT work in the morning?
(He told me that you might also find the combination 'arriving to work')
Bob is a very fast runner. He can run 100 metres IN 10 seconds.
What are you doing ON the weekend?
There are usually a lot of parties ON New Years Eve.
I havent seen Kate for some time. I last saw her at Daves wedding.
I also found online an information about it with a chart for the prepositions and examples. You might wanna have a look at it: