With how little of a boost Speed Booster really gives, I think it would be fine to have it as a side effect of Amplified, active for the whole Amplified duration. It's a little silly that it takes around 3 or 4 seconds to activate while sprinting while Amplified. It makes the subclass feel slower, which is not what Arc is supposed to be. It would also be nice if it applied to normal walking instead of just sprinting. Really build into the movement aspect of Arc. Maybe this could be a fragment!
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No it shouldn't, but it should definitely activate quicker.