Graph the velocity (in ft/s) according to the following function:

$v(t) =\left\{ \begin{array} { c c } { 2 t } & { \text { for } 0 \leq t \leq 10 } \\ { 20 } & { \text { for } 10 < t < 20 } \\ { - 2 t + 60 } & { \text { for } 20 \leq t \leq 30 } \end{array} \right.$

1. What would the area under the curve represent?

   Hint (a):

   What are the units on the axes? Multiply these units.

2. Calculate the area under the curve.

   Hint (b):

   Use familiar geometric shapes.

3. How does this relate to a position graph?