Michelle started walking at $3$ ft/s and steadily increased her speed so that she was walking $6$ ft/s after $300$ seconds.

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

   Answer (a):

   

2. Write the equation of this line.

   Hint (b):

   Find the slope of the line and the y-intercept. Write the equation in $y = mx + b$ form.

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

   Hint (c):

   Find the area under the curve after $1$ minute and then after $5$ minutes.

   Partial Answer (c):

   $198$ feet

4. How far did Michelle walk in $T$ seconds for $0 ≤ T ≤ 300$?

   Answer (d):

   $A = \frac{1}{2}(3 + (3 + 0.01T ))T = 3T + 0.005T ^{2}$