I have V-brakes on my Fuji Absolute, and there is a little play in the brake arms. I tightened the mounting bolt that connects the mounting bolt to the brake studs but it still has some play. Is this normal? If not, how would I go around fixing it?
This is quite normal. Each brake arm slips over the mounting post on the frame and pivots on it, but the limit on tightening the bolts are when they hit the posts, not when they clamp the arms rigidly to the fork. If they did that overtight would stop the brakes working, but also the bolts would have to be loose for the brakes to work, so they'd come undone over time. The diagram below is the best I could find, so for what it's worth... brake arms, bolt and fork plus a bunch of other bits...
(Via bicycling.com forums "exploded view of the CX70 brakes from the Techdocs site"
Note that these are cantilever brakes not V brakes, but they work the same way. V brakes don't have the saddle (part 4) though.