The two-dimensional motion of a particle is described by the position vector r = R ( t) i + R ( t) j . The motion of this particle is a/an: A. straight line path B. circular path C. simple harmonic motion D. periodic motion Choose the correct answer from the options given below:

Step-by-step solution

Given position vector r = R ( t) i + R ( t) j The coordinates of the particle are x = R ( t) and y = R ( t) Squaring and adding both equations gives x^2 + y^2 = R^2 ( ^2( t) + ^2( t)) = R^2 This is the equation of a circle with radius R centered at the origin. Thus, the particle moves in a circular path. Since the motion is uniform circular motion with constant angular velocity , it repeats itself after a fixed interval of time T = 2 . Therefore, the motion is periodic. The motion is not simple harmonic because sim