A particle travels in the X-Y plane governed by the equation r = ( i + 2 j ) A t . The motion of this particle is

Step-by-step solution

Given position vector r = ( i + 2 j ) A t The x and y coordinates of the particle are: x = A t y = 2A t Eliminating t , we get: y = 2x This is the equation of a straight line passing through the origin, so the particle moves on a straight line. Differentiating r with respect to time t to find acceleration: v = d r dt = -( i + 2 j ) A t a = d v dt = -( i + 2 j ) A ^2 t a = - ^2 r Since the acceleration is directly proportional to the negative of the position vector, the motion is simple harmonic. Every simple harmon