Question

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

Answer 1

`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`