The positions of two particles, A and B, moving along a straight line (x-axis) are given by the equations x_A = 4t^2 + 2t - 5 and x_B = 4t^2 + 2t + 3 , where x is in meters and t is in seconds. Which of the following statements correctly describes the state of particle A with respect to an observer on particle B?

Step-by-step solution

The position of particle A is given by x_A = 4t^2 + 2t - 5 The position of particle B is given by x_B = 4t^2 + 2t + 3 The relative position of particle A with respect to particle B is: x_ AB = x_A - x_B x_ AB = (4t^2 + 2t - 5) - (4t^2 + 2t + 3) = -8 m The relative velocity of particle A with respect to particle B is: v_ AB = dx_ AB dt = d dt (-8) = 0 m/s Since the relative velocity is zero at all times, particle A is permanently at rest with respect to particle B. Answer: Particle A is permanently at rest with resp