Math 251 Week 5 Written Assignment (25 Points)When this assignment is completed, be sure to scan it and save it as a PDF, then upload it to Moodle by the deadline.Part 1: This week you have been learning about higher order derivatives and their meaning. Focus on measurement units and what is physically going on in this scenario. You may use Desmos to help you sketch and visualize graphs. If you are asked to calculate anything, show your algebra. Provide all measurement units in responses.The Situation: We will begin time at the moment you leave your classroom on campus. The classroom is 5 miles from your home. You are tired since you just finished taking your calculus test and you pedal your bicycle in the opposite direction from home for a while. Later you turn around and head toward home again, but since you are dehydrated, you end up turning around again a short time later. After 5 hours you stop.Let \( s(t)\) be your distance (in miles) from home at time \( t \)(hours).\[s(t)=t^{3}-8 t^{2}+16 t+5\]This position function is graphed next and linked in Desmos for your convenience.