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?

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.