Why are pads on linear-pull brakes so much longer?

I've had a few bikes with a couple of different brake systems on them in the past. I have noted that of all of them, linear-pull ("V") brakes always seem to have distinctively long pads. Why is this? Is there something about the mechanics of that sort of brake that requires a longer pad (so long that it follows the wheel's arc, even) as compared to seemingly every other form of rim-brake?