The position function of a particle in rectilinear motion is given by s(t) s(t) = t3 – 9t2 + 24t + 1 for t ≥ 0. Find the position and acceleration of the particle at the instant the when the particle reverses direction. Include units in your answer.

Answer 1

it reverses direction when v changes from + to -

v(t) = 3t^2-18t+24 = 3(t^2-6t+8) = 3(t-2)(t-4)

So, where does v(t) cross the axis and become negative?

Now use that value to find s(t) and a(t)