You are a Spell Forge in the Harry potter universe. By adding a sound of "aaaa" of x seconds at the end of a chant you can accelerate the spell by a m/sec?. However a spell is cast at the end of the chant and thus will take x seconds longer to cast. The spell you are currently working on moves at a constant velocity of 2m/s when no "aaa" sound is attached to it. Note: The spell only starts moving after you complete your chant which includes any "aaa" you intend to add. Q3.1 velocity What will the velocity of the spell be as a function of time it you suffix an "aaa" of 1 sec to the chant? (take t = 0 at the moment the chant ends) Show your Work.

You are a Spell Forge in the Harry potter universe. By adding a sound of "aaaa" of x seconds at the end of a chant you can accelerate the spell by a m/sec?. However a spell is cast at the end of the chant and thus will take x seconds longer to cast. The spell you are currently working on moves at a constant velocity of 2m/s when no "aaa" sound is attached to it. Note: The spell only starts moving after you complete your chant which includes any "aaa" you intend to add. Q3.1 velocity What will the velocity of the spell be as a function of time it you suffix an "aaa" of 1 sec to the chant? (take t = 0 at the moment the chant ends) Show your Work.