4.3.3Is your teacher guilty?

The judge has accepted your arguments and has thrown out the evidence displayed in Exhibit B and Exhibit C. However, the prosecution has not yet given up. They have brought in a new expert who has direct evidence against your teacher.

Prosecution: “While it is highly distressing that this court has decided to throw out our main evidence on a mere technicality, we are convinced that we have enough additional evidence to prove the guilt of the defendant. In addition to our cameras, we used a plane to keep track of the defendant’s velocity. We would now like to call our final witness to the stand, Officer Rongway of the Highway Patrol.”

Officer Rongway: “I spotted the defendant leaving Accelerton at 3:20 p.m. I utilized our new air tracking system to graph the velocity of the vehicle as the defendant made the $100$-mile trip from Accelerton to Geprime. This can be seen in Exhibit D. On the graph, the portions of the curve that exceed the $65$ mph speed limit identify the infractions. As you can see, the defendant violated the law several times.”

Judge Ironhand: “I am granting the defense’s request for a recess so that they may review the last bit of evidence presented by the prosecution. You may use this evidence along with Exhibit A to complete your analysis. I expect both sides to wrap up their arguments so that I can make a judgment on this drawn out case.”

Your Task: Analyze the final evidence presented by the prosecution. Is it accurate? Can you find a way to spare your teacher’s (and your own) fate, or should you beg for mercy? Write your closing arguments. Be sure to address each of the exhibits presented by the prosecution. Remember, you are defending your teacher.

Make sure that your conclusions are accurate since Judge Ironhand stated he will come down hard on any conclusion based on an estimate.

$v ( t ) = \left\{ \begin{array} { l l } { - 187.5 t ^ { 2 } + 150 t + 45 } & { \text { for } 0 \leq t < 0.7 } \\ { 43.75 t + 27.5 } & { \text { for } 0.7 \leq t < 1.2 } \\ { - 500 t ^ { 2 } + 1200 t - 640 } & { \text { for } 1.2 \leq t < 1.6 } \\ { 7500 t ^ { 2 } - 25500 t + 21600 } & { \text { for } 1.6 \leq t < 1.8 } \\ { - 528 t ^ { 2 } + 2284.8 t - 2402 } & { \text { for } 1.8 \leq t \leq 2.3 } \end{array} \right.$