The gap between two consecutive automobiles (distance between the back of a vehicle and the front of the following vehicle) is 65 ft. At a certain time the front vehicle is traveling at 40 mi/h and the following vehicle at 30 mi/h. If both vehicles start accelerating at the same time, determine the gap between the two vehicles after 10 sec if the acceleration of the vehicles can be assumed to take the following forms:

where u_t is the vehicle speed in ft/sec.

du = 3.4 0.07u, (leading vehicle) dt du dt -= 3.3 -0.065u, (following vehicle)