Is there a noticeable advantage in f/1.8 over f/2?

I have a bit of a complicated question.
On short notice I will be photographing a greyhound race, at night in a moderately lit track.
I currently have a Nikon D7000 with kit 18-105 3.5/5.6 and a 60mm f/2.8D.
I would like to get a faster lens as I'm concerned f/2.8 on the 60mm might be too slow to achieve shutter speeds that won't blur.
I might be able to get some $$ for a 50 1.4 but I doubt it.
so 35mm f/2, 35mm f/1.8

Yes the f/1.4 would be the best choice. I used to shoot video at a grey hound track and I know what the lighting is like - not good at all. You might get by with the f/1.8 but it would be iffy going in.
If you shoot under or near one of the track side lights at full aperture and 1/500 you might be able to cut the blur to a minimum. But again, certainly the f/1.4 would be best. I do understand they're
expensive for one job. But you may be able to use it to advantage later.

I know, I'm doing the exact same thing considering a Canon eos t1i for a special job. I empathize with what your going through right now.

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