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Find the velocity function in terms of t (in seconds)

Find the velocity function in terms of t (in seconds)-example-1

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s(t)=(2)/(3)t^3-(9)/(2)t^2-18t

The velocity function is given by the derivate of the position function.

Then, find the derivate of s(t) to find the velocity function:


\begin{gathered} v(t)=(d)/(dt)(2)/(3)t^3-(d)/(dt)(9)/(2)t^2-(d)/(dt)18t \\ \\ v(t)=(2)/(3)((d)/(dt)t^3)-(9)/(2)((d)/(dt)t^2)-18((d)/(dt)x) \\ \\ v(t)=(2)/(3)(3t^2)-(9)/(2)(2t)-18(1) \\ \\ v(t)=2t^2-9t-18 \end{gathered}

Then, the velocity function is:


v(t)=2t^2-9t-18

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