A particle moving along the x axis has a position given by x = (24t - 2.0t³) m, where t is measured in s. What is the magnitude of the acceleration of the particle at the instant when its velocity is zero? A) 24 m/s² B) zero C) 12 m/s² D) 48 m/s² E) 36 m/s²

Question

Quizplus · Accepted Answer

The acceleration of the particle is the second derivative of its position with respect to time. The given position function is x = 24t - 2.0t^3. The first derivative, which gives the velocity, is v = dx/dt = 24 - 6t^2. Setting this equal to zero to find when the velocity is zero gives 24 - 6t^2 = 0, solving for t gives t = 2 seconds. The second derivative, which gives the acceleration, is a = d^2x/dt^2 = -12t. Substituting t = 2 seconds into the acceleration equation gives a = -12(2) = -24 m/s^2. The magnitude of the acceleration is 24 m/s^2, indicating choice A is correct.

A Particle Moving Along the X Axis Has a Position