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?
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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:
(The entire section contains 185 words.)
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