You have a modern vehicle with a good brake and tires. A child runs onto the road 40m ahead of you while you are traveling in a 55km/h zone. You brake hard. Will you stop in time? Table 1. Braking distances for five types of car at different initial speeds Speed Speed Braking (km/h) (m/s) Distance Ferrari 550 Lexus Mercedes Nissan Toyota Maranello LS400 C36 2005X Corolla 0 0 0 0 0 10 2.8 0.4 0.6 0.4 0.5 0.7 20 5.6 1.7 2.2 1.8 1.9 2.8 30 8.3 3.7 5 4 4.3 6.2 40 11.1 6.6 8.9 7.1 7.6 11 50 13.9 10.4 14 11.1 11.9 17.2 60 16.7 14.9 20.1 16 17.2 24.8 70 19.4 20.3 27.4 21.8 23.4 33.8 80 22.2 26.5 35.8 28.4 30.6 44.1 90 25 33.6 45.3 36 38.7 55.8 100 27.8 41.5 $5.9 44.4 47.8 68.9 110 30.6 50.2 67.7 53.8 57.8 83.4 120 33.3 59.7 80.5 64 68.8 99.2 A) Find a mathematical model/formula to answer the question. What assumptions do you make to create a mathematical model? B) What are limitations of your model? What are the factors you did not consider for your model