The fastest time ever run at pikes peak is 7: 57. that’s way too long. if we removed all the curves, making a straight line from top to bottom, how quickly could a redeye reach the top?

protips:
slope of 6.4%
redeye top speed 203 mph
a stock redeye has a peak acceleration of over 1g. assume this redeye will accelerate at an average of .091 g (2.93 ft/s2)
the 12.42 mile long pike’s peak course has over 156 turns

what you might need:
(unit conversions)
a smart friend
some kinematic equations:
d=v^2/2a
t=v_f/a
t=d_remaining/v_f

  4 minutes 31.06 seconds

Step-by-step explanation:

We can start by converting the speed and distance to units compatible with the acceleration.

  12.42 mi = (12.42 mi)(5280 ft/mi) = 65,577.6 ft

  203 mi/h = (203 mi/h)(22/15 ft/s)/(1 mi/h) = 297 11/15 ft/s = 4466/15 ft/s

Then the time taken to reach top speed will be ...

  t = v_f/a = (4466/15 ft/s)/(2.93 ft/s^2) = 101.615 s

The distance covered while reaching top speed is ...

  d = v^2/(2a) = (4466/15 ft/s)^2/(2(2.93 ft/s^2)) = 15,127.157 ft

So, the remaining distance is ...

  d_remaining = 65,577.6 ft -15,127.157 ft = 50,450.443 ft

And the time required to cover that distance is ...

  t = d_remaining/v_f = (50,450.443 ft)/(4466/15 ft/s) = 169.448 s

The total time taken for acceleration and cruise to the top is ...

  101.615 s + 169.448 s = 271.064 s ≈ 4 minutes 31.06 seconds

We have assumed that the rocket's acceleration is fully applied in the direction of travel. We have to assume that the acceleration due to gravity is otherwise accounted for.