1) I hit a bowling ball with the mallet. It starts from rest (not moving). Suppose every time I hit it, its velocity increases by 10 cm/s (v=10 cm/s), and I hit it so it moves in a straight line. You start timing, t = 0 seconds, at the instant I hit the ball the first time, and I hit it once every second. Let's make two simplifying approximations: (1) Suppose each hit is very quick, so the speed changes "instantly." (2) Suppose the ball rolls on a very smooth surface, so that it doesn't slow down between hits. So for 1 second, it moves 10 cm/s, for the next second it moves 20 cm/s, and so on. A. Start with everyday thinking, as in "think like a 10-year-old": How far will the ball move from its starting position in 3 seconds? How far in 6 seconds? B. Someone might have the automatic reaction that twice the time means twice the distance. When would that reasoning be correct, and why isn't it correct in this case? C. OK, first math of the course! (Well, unless you've watched FlipIt already.) It's for you to come up with a formula. What's an expression for how far the ball will go in n seconds (n is an integer). D. Suppose I change my technique. I ease up how hard I hit the ball, so that now it speeds up 5 cm/s with every hit. But I hit it twice as often, once every halfsecond instead of once a second. Start the clock again at the instant I hit the ball the first time, starting from rest. Will the ball move the same distance as in part a, in 3 seconds? In 6 seconds? Farther? Not as far? Explain why...