The coordinates of an object moving in the xy plane vary with time according to

Question

The coordinates of an object moving in the xy plane vary with time according to the equations x = ?4.75 sin ?t and y = 4.00 ? 4.75 cos ?t, where ? is a constant, x and y are in meters, and t is in seconds. (a) Determine the components of velocity of the object at t = 0. (Use the following as necessary) (b) Determine the components of the acceleration of the object at t = 0. (Use the following as necessary: ?.) (c) Write expressions for the position vector, the velocity vector, and the acceleration vector of the object at any time t > 0. (Use the following as necessary: omega for ? and t.)

Explanation / Answer

B. v and a are the 1st and 2nd derivatives of position. Position = (-5sin?t, 4-5cos?t) m 1st deriv. v = (-5?cos?t, +5?sin?t) m/s 2nd deriv. a = (+5?^2sin?t, +5?^2cos?t) m/s^2 A. Just evaluate above for t=0; cos functions will be 1 and sin functions 0. p = (0, -1) m v = (-5?, 0) m/s a = (0, 5?^2) m/s^2 C. The path is clockwise around a circle of radius 5 m centered at (0,4) m, starting at the lowermost point on the circle.

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