Find parametric equations for the path traced out by a specific point inside the

Question

Find parametric equations for the path traced out by a specific point inside the circle as the circle rolls from left to right. (Hint: If r is the radius of the circle, let d < r be the distance from the point to the center.) Find the minimum and maximum speeds of the point and the locations where each occurs. Graph the curve for v=3, r=2, and d=1. This curve is called a trochoid.

Explanation / Answer

Avg Speed = TOTAL Distance traveled / TOTAL Time to travel that Distance {confusion arises because we use the term "velocity" when it is more accurate to call it "speed" since we want students to know that velocity is a VECTOR quantity requiring a DIRECTION as well as a SIZE) This is not UR fault but that of the wording of the question - whoever created that :>) p/s In a "straight line" is not sufficient to be called DIRECTION since one dimensional travel still has two directions (+/-) possible. So what was really given in this question was the jogger's SPEED. multiply speed x time convert all times to seconds (basic unit of time in SI system) 3.8 x 2.6 x 60 = 593 m 5.5 x 4.1 x 60 = 1353 m total Distance traveled = 593 + 1353 = 1946 = 1900 m

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