Question

The position function of a particle in rectilinear motion is given by s(t) = 2t^3 - 21t^2 + 60t + 3 for t ≥ 0. Find the position and acceleration of the particle at the instant when the particle reverses direction. Include units in your answer.

So I've already gotten the first derivative(6t^2-42t+60) and set it to 0. this resulted in t=5 and t=2. I then took the second derivative(12t-42) and plugged in t for acceleration. Where do I go from here?

Answer 1

Your first and second derivatives which are the velocity and the acceleration respectively are correct.
The particle has reverses direction when v(t) ≤ 0 so at interval 2 < t < 5 sec.
You can substitute now t = 2 for s(2) and a(2) for first changing direction. Also t = 5 for s(5) and a(5) for second changing direction.