To get to work, a man has a one$-$hour commute on the interstate. Although he starts out at over $70$ mph $,$ the heavy volume of cars causes a minor slow$-$down so he's going approximately $60$ mph after $40$ minutes. His speed is governed by the function:

Speed $=25**(t-0\mathrm{.}7{)}^2+60$

where speed is in mph and $t$ is in hours.

Objective A

Create the subplots below depicting the speed on the top graph and the acceleration $($derivative of speed function$)$ on the bottom graph. The functions should be plotted on the interval from $0$ to $1(x$ values$)$ as shown. The speed plot should have the area under the first half$-$hour shaded one color and the area under the second half hour shaded a different color $($for visualization of Objective B$).$

Obiective B

Integrating the speed function yields the distance traveled. Use MATLAB to calculate the distance traveled in the first half hour and the distance traveled in the second half hour.