2) A car is traveling at 80 feet per second when the driver spots a deer in the road 150 feet ahead and slams on the brakes. The car's speed at the given times is shown in the table below, where time is measured in seconds since the driver applied the brakes, and speed is measured in feet per second. ----n S-eed, v (ft/sec.) mum-\"n a) Sketch the graph of the table given above and use five rectangles to estimate the maximum distance that the car will travel on the interval [0, 2.5] after the brakes are applied. b) If the deer freezes and does not move, will the car hit the deer? Explain. c) If, instead of slowing down as shown in the table above, the car slows at a constant rate of 16 feet per second per second after the brakes are applied, would the car hit the deer? Explain. 3) Police Chase: A speeder traveling 40 miles per hour (in a 25 mph zone) passes a stopped police car, which immediately takes off after the speeder. If the police car speeds up steadily to 55 miles/hour in 10 seconds and then travels at a steady 55 miles/hour, how long and how far before the police car catches the speeder who continued traveling at 40 miles/hour? See figure below. [Find the total distance traveled of each by considering the area under the curves. Pay attention to the units of time.] 65- 60- velocity (miles/hour) 55- 50- 45- 40 35- 30+ 25+ 20+ 15+ 10+ 5+ 40 50 10 20 30 t (seconds)