Question-1) [Total 20 points] A position vector of a particle with mass m is given by I (t) = A cos(ot) + A sin(ot) as a function of time. Amplitude A and angular frequency o are constant. (Part a) [2 points] What is the initial position vector, r. which is the position at time t = 0? (Part b) [3 points] What is the displacement vector, Ar (t) of at the particle between initial time t = 0 and at a later time t = t/o ? (Part c) [5 points] What is the velocity vector v (t) and acceleration vector a (t) of the particle as a function of time? (Part d) [5 points] What is the angle between the acceleration (t) and the position (t) of the particle? What is the angle between the velocity v (t) acceleration a (t) of the particle? and the (Part e) [5 points] According to relations between the acceleration a (t) and the position r (t) as well as between the velocity V (t) and the acceleration a (t), how can you describe this motion? Explain your answer with reasons.