The motion of a particle is defined by the equations x 6t 3 sin t and y 6 3 cos t, where x and y are expressed in meters and t is expressed in seconds Sketch the path of the particle for the time interval 0 t 2, and determine (a) The magnitudes of the smallest and largest velocities reached by the particle, (b) The corresponding times, positions, and directions of the velocities

Question: The motion of a particle is defined by the equations x = 6t 3 sin t and y = 6 3 cos t,

The motion of a particle is defined by the equations x = 6t − 3 sin t and y = 6 – 3 cos t, where x and y are expressed in meters and t is expressed in seconds. Sketch the path of the particle for the time interval 0 ≤ t ≤ 2π, and determine

(a) The magnitudes of the smallest and largest velocities reached by the particle,

(b) The corresponding times, positions, and directions of the velocities.

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