Question

A particle is moving along the x-axis for t>=0. The position of the particle is given by x(t)=t³-9t²-21t+6. At what time t, does the particle change directions?

Answer 1

The particle changes directions at t = 3.96 s.

Step-by-step explanation:

To determine at what time the particle changes directions, we need to find when the velocity of the particle becomes zero. The velocity of the particle can be found by taking the derivative of the position function with respect to time. Taking the derivative of x(t)=t³-9t²-21t+6, we get v(t)=3t²-18t-21. Setting v(t) equal to zero and solving for t:

0 = 3t²-18t-21

Using the quadratic formula, we find t = 3.96 s. Therefore, the particle changes directions at t = 3.96 s.