The problem statement, as written, has a few ambiguities in it. The main one regards what is meant by "if we removed all the curves ... ."
Interpretation A:
Keep the 3-dimensional starting location and finish location exactly where they are, and then draw a new, straight line between them, and that is the new track.
However, this will increase the slope above 6.4 %, if that even matters.
Without knowing more information the relative position between the starting location and finish location, there isn't enough information to solve this problem, in this interpretation.
Interpretation B:
Grab the starting position and pull it out horizontally until the track becomes a taught, straight line. In this interpretation, the length of the track is still 12.42 miles and the slope is still 6.4% (if the slope even matters).
Other ambiguities:
The maximum acceleration is specified as 2.93 \ \mathrm{\frac{ft}{s^2}}. But is this the maximum acceleration with respect to the road
when climbing a 6.4% slope, or 2.93 \ \mathrm{\frac{ft}{s^2}}
total?
You see, initially when the vehicle is accelerating, it will be fighting the acceleration of gravity somewhat due to the fact that it's on a slope. Should this be taken into account,
or is it already taken into account in the 2.93 \mathrm{\frac{ft}{s^2}} specification?
Also, I looked up the
Pikes Peak International Hill Climb. Its track length is 12.42 Miles with an elevation change (from start to finish) of 4725 ft. That produces an average slope gradient of 7.22%, although this problem says to use only 6.4%, and honestly, I'm not certain whether the slope is relevant to solving this problem at all, given the other ambiguities.
