The function shown below was created to track the different intervals of speed that an automobile travels over a period of 28 seconds. Use the graph of the function to complete Parts 1-3. After traveling for 16 seconds, the automobile begins to slow its speed at a steady rate. Use the coordinates on the graph to determine the rate at which the car is slowing down, in miles per hour per second. During which interval of time does the automobile experience the greatest change in its speed? What is the change in the automobile’s speed during this interval? For a time period of approximately 10 seconds, the automobile experiences no change in its speed. During which interval of time does the automobile’s speed remain constant? At what speed is the automobile traveling during this interval?

Answer:1. The car is slowing down at a rate of 2.5mph/s2. The greatest acceleration is 10 mph/s.3. In the interval 4s to 16s the speed remains constant and has magnitude 25 mph.Step-by-step explanation:1. The deceleration of the car is from 16 seconds to 24 seconds is the slope [tex]m[/tex] of the graph from 16 to 24: [tex]m=\dfrac{\Delta speed }{\Delta time } = \dfrac{5-25}{24-16} =-2.5mph/s[/tex]the negative sign indicates that it is deceleration. 2. The automobile experiences the greatest change in speed when the slope is greatest because that is when acceleration/deceleration is greatest.From the graph we see that the greatest slope of the graph is between 28 and 24 seconds. The acceleration the interval is the slope [tex]m[/tex]:[tex]m= \dfrac{45-5}{28-24}= 10mph/s[/tex]3. The automobile experiences no acceleration in the interval 4 s to 16 s—that's the graph is flat. The speed of the automobile in that interval, as we see from the graph, is 25 mph.