Toby is driving a 2021 Honda Insight at 45 mi/h along a straight road and then slows down at a constant rate of 11 ft/sec²_,

(a) Write an acceleration function a(t) for this problem, where t= 0 corresponds to the moment Toby hits the brakes.

(b) Write the most general velocity functionv(t) associated with this acceleration function.

(c) The initial velocity was 45 mi/hr which is equivalent to 66 ft/sec. Use this information to write the particular velocity function for this problem.

(d) Write the position function s(t) for this problem. Let s(0) = 0.

(e) At what time t does Toby's car come to a stop? Hint: When it stops, v(t) = 0.

(f) How far does the car travel from the moment Toby hits the brakes until the moment the car comes to a stop?