The position function of a particle in rectilinear motion is given by s(t) s(t) = t^3 - 9t^2 + 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 its velocity changes sign. That is, when v(t) = 0.

So, find t when

v(t) = s'(t) = 3t^2 - 18t + 24 = 0

then plug that value into s(t) and a(t)