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 below:
where ut is the vehicle speed in ft/sec.
What will be an ideal response?
First, determine the distance each vehicle travels during the elapsed time (10
seconds) using Equation 3.12. For the leading vehicle:
Similarly, for the following vehicle:
Since the leading vehicle traveled further, the gap between vehicles increased by the difference in the distances, 559.27 – 458.65 = 100.62 ft.
The initial gap was given as 65 ft, so after 10 sec, the gap is 65 + 100.62 = 165.62 ft.
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