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1. The parametric equations of an object are given by x = Rcos(wt), and y-Ksin(ot), where x and y are measured in meters and t in seconds. Assume R and ω are known. Calculate the following: (a) The radius of curvature ρ when x = 0.5K meter. Do it by applying the formula ラク dxz (b) The magnitude of the velocity as function of time (c) The x and y components of the acceleration as function of time.( ax-a,-?) (d) The magnitude of the acceleration as function of time (e) The radial ar and transverse component of the acceleration aθ as function of time. () The tangential a, and normal an components of the acceleration as function of time. (g) when the time is t = π/2ω draw and label on the trajectory the vectors ur and ul. (h) when the time is t = π/2ω draw and label on the trajectory, the vectors ui and ue. (i) How the magnitude of the acceleration as function of time changes when one goes from the rectangular x and y system to the polar coordinates, and to the normal and tangential coordinates?
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