Motion along a curve   a) a(t) = <2t, 2sin(t), cos(4t) >. At t = 0, the velocity is <1, -3, 2> and the position is <2, -1, -1 >. Find v(t) and r(t).

Calculus I Derivatives Instantaneous velocity

PART A Let x(t) = 5 cos(t) and y(t) = 3 sin(t) At t = 6, x(6)= = y(6) = speed (6) PART B Now, if we let r(t) = 5 cos(2t) and y(t) = = 3 sin(2t), we have the same path: And at t (3) = = = = = 3 y (3) Do you see how it's the same point as PART A? speed (3) = Is speed in PART B slower or faster than the speed in PART A? Select an answer ✓ ELLIPSE 2 ELLIPSE 2

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