The velocity of a particle moving along the x axis is given for t 0 by vx = (32.0t − 2.00t3) m/s, where t is in s. What is the acceleration of the particle when (after t = 0) it achieves its maximum displacement in the positive x direction? A)−64.0 m/s² B)zero C)128 m/s² D)32.0 m/s² E)−32.0 m/s²

Question

The velocity of a particle moving along the x axis is given for t > 0 by vx = (32.0t − 2.00t3) m/s, where t is in s. What is the acceleration of the particle when (after t = 0) it achieves its maximum displacement in the positive x direction? A)−64.0 m/s² B)zero C)128 m/s² D)32.0 m/s² E)−32.0 m/s²

Quizplus · Accepted Answer

The maximum displacement occurs when the velocity is zero. Setting vx = 0 gives 32.0t - 2.00t^3 = 0, solving for t gives t = 4 s. The acceleration is the derivative of velocity: a = dvx/dt = 32.0 - 6.00t^2. Substituting t = 4 s gives a = 32.0 - 6.00(4)^2 = -64.0 m/s².

The Velocity of a Particle Moving Along the X Axis