# Let s(t) = t^3 - 9t^2 + 24t be the position function of a particle moving along a coordinate line where s is in meters and t is in minutes. At what time is the particle stopped and when is the...

Let s(t) = t^3 - 9t^2 + 24t be the position function of a particle moving along a coordinate line where s is in meters and t is in minutes.

At what time is the particle stopped and when is the particle speeding up or slowing down?

sciencesolve | Certified Educator

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You need to evaluate derivative of the function `s(t)`  to check when the particle speeds up or slows down or even stops.

Hence, differentiating `s(t)`  with respect to t yields:

`s'(t) = (t^3 - 9t^2 + 24t)'`

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

You need to check when the particle stops, hence, you need to solve the equation `s'(t) = 0`  such that:

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