A driver traveling on an interstate highway sees traffic coming to a stop ahead and appl...

A driver traveling on an interstate highway sees traffic coming to a stop ahead and applies the brakes. The car’s speed, in feet per second, is given by

a. Make a sketch of the speed curve for t ≥ 0.

b. How long does it take for the car to come to rest?

c. Make a table of speeds starting from time t = 0, the instant when the driver applies the brakes, including every half-second until the car comes to rest.

d. What is the slowest the car is traveling in the first half-second after the brakes are applied? What is the fastest the car is traveling in the first half-second?

e. Repeat part (d) for the second half-second and the third half-second.

f. What is the minimum distance the car can travel in the first half-second? In the second half-second? What is the maximum distance the car can travel in the first half-second? In the second half-second?

g. Use the table from part (c) to estimate a lower and an upper bound on the distance it takes for the car to come to rest.