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

what you want is the moment when the particle changes direction. That is, when v(t) = 0. t=2 is the first such time, so you just want

s(2) = 55
a(2) = -18

Makes sense, since the velocity is changing from + to -, that the acceleration would be negative.

If you want the values when t=5, just plug that in.