Problem 3: A particle tied to a rope is traveling in uniform circular motion. Ignore the force of weight (this is out in space). The position of the particle is given by: (t) = (cos 3t, sin 3t, 0) m y Rope X The particle has a mass of 5 kg. Given this information, answer the following questions: i) What is the velocity of the particle as a function of time t? ii) What is the speed of the particle? iii) What is the force acting on the particle? Hint: Work in normal and tangential coordinates. iv) What is the impulse by the rope on the particle over the interval 0 t 2? 2 3