Question

The velocity of particle moving along x axis is given T>0 by V_x=(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?

Answer 1

To find the time at which the displacement is the maximum, equate velocity to zero. Then find the derivative of velocity t get the acceleration.

$$v_x=30t-2t^3=0,\\ t=3.87\text{ s},\\ a_x(t)=30-6t^2→a(3.87)=15\text{ m/s}^2.$$