Michelle starts walking at a rate of $3$ ft/s and steadily increases her speed so that she is walking at a rate of $6$ ft/s when $t = 300$ seconds.

1. Sketch a graph showing Michelle’s velocity as a function of time.

   Hint (a):

   Your curve should contain the points $\left(0, 3\right)$ and $\left(300, 6\right)$.

2. Write the equation of the curve in your graph from part (a).

3. Show that Michelle walked $198$ feet in the first $1$ minute and $1350$ feet in the first $5$ minutes.

   Hint (c):

   This is the area under the curve, which is a trapezoid.
   Be sure to convert minutes to seconds before making your calculations.

4. How far did Michelle walk in $t$ seconds for $0\le t\le300$?