5. while driving home on the taconic state highway, ernesto hits some light traffic that makes him slow…

5. while driving home on the taconic state highway, ernesto hits some light traffic that makes him slow down. after getting out of the light traffic, he is able to speed up for a short time before he eventually has to slow to a complete stop. (a) during the time that ernesto is speeding up, what is the rate of change of his speed? include units in your answer. (b) is ernestos speed changing faster when he slows down initially or when he comes to a complete stop? justify your response.

5. while driving home on the taconic state highway, ernesto hits some light traffic that makes him slow down. after getting out of the light traffic, he is able to speed up for a short time before he eventually has to slow to a complete stop. (a) during the time that ernesto is speeding up, what is the rate of change of his speed? include units in your answer. (b) is ernestos speed changing faster when he slows down initially or when he comes to a complete stop? justify your response.

Answer

Explanation:

Step1: Calculate the rate of change

The rate of change (slope) formula is (m=\frac{y_2 - y_1}{x_2 - x_1}). For the speeding - up part, we have two points ((0,72)) and ((3,45)). [m=\frac{45 - 72}{3-0}=\frac{- 27}{3}=-9] The units of the rate of change is miles per hour per minute.

Step2: Analyze the slope for slowing - down

For the slowing - down part (points ((9,45)) and ((11,30))), the slope is (m=\frac{30 - 45}{11 - 9}=\frac{-15}{2}=-7.5)

Since (\vert-9\vert>\vert-7.5\vert)

Answer:

(a) The rate of change of his speed is (-9) miles per hour per minute. (b) Emesto's speed is changing faster when he slows down initially. Because the magnitude of the slope (rate of change) when speeding up ((\vert-9\vert)) is greater than the magnitude of the slope when coming to a complete stop ((\vert-7.5\vert))