You are a Spell Forge in the Harry potter universe. By adding a sound of "aaaa" of a seconds at the end of a chant you can accelerate the spell by x m/sec2. However a spell is cast at the end of the chant and thus will take z 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 2 Points 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. Q3.2 position 3 Points What will its position be as a function (p(t)) of time? (t = 0 is the moment the chant ends) Show your Work. Q3.3 best "aaa" 3 Points If your target is 10m away will the "aaa" benefit you? (assuming you want to minimize the total time it takes for the spell to hit the target(including the time it takes to finish the chant)) Explain your reasoning.