The position function of a particle in rectilinear motion is given by s(t) = t3 – 12t2 + 45t + 4 for t ≥ 0 with t measured in seconds and s(t) measured in feet. find the position and acceleration of the particle at the instant when the particle reverses direction. include units in your answer.

With position function

the velocity of the particle is given by

The particle changes direction when its velocity changes sign. We have

so the particle's direction is reversed at two different times.

The acceleration is given by

When , the particle's position is ft and its acceleration is ft/s^2.

When , the particle's position is ft and its acceleration is ft/s^2.

step-by-step explanation:

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