Question

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

Answer 1

$s(t)=\frac{2}{3}t^3-\frac{9}{2}t^2-18t$

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

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

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

Then, the velocity function is:

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