The instantaneous speeds for two rocket cars are given by a(t) = t^2 -8t + 18 and b(t) = -2t + 13, where t is in minutes and speeds are in miles per minute. Let A(t) and B(t) represent the respective distances traveled for the two cars, since we measure distance traveled from t = 0, you may assume that A(0) = 0 and B(0) = 0. a) Give the formulas for distance traveled.
b) Find the time in the first ten minutes when Car B is ahead of Car A by the greatest distance and determine that distance.
c) Determine the lowest speed at which Car A ever travels. Include units.
d) write an equation that you in order find the times when one car passes the other put your equation in the form
e) Determine two times at which Car A is traveling at a rate of 8 miles per minute. (Round to two digits after the decimal.)
f) How far does car e travel during the time interval from t = 2 to t = 8? Include units.