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 car reach the top?
protips:
slope of 6.4%
car top speed 203 mph
a stock car has a peak acceleration of over 1g. assume this car 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

271.4 s

Explanation:

We are told the top speed (maximum speed) the car has is:

taking into account

And the car's average acceleration is:

Since:

(1)

Where:

is the car's final speed (top speed)

because it starts from rest

is the time it takes to reach the top speed

Finding this time:

(2)

(3)

(4)

Now we have to find the distance the car traveled at this maximum speed with the following equation:

(5)

Isolating :

(6)

(7)

(8)

On the other hand, we know the total distance traveled by the car is:

Hence the remaining distance is:

(9)

(10)

So, we can calculate the time it took to this car to travel this remaining distance at its top speed , with the following equation:

(11)

Isolating :

(12)

(13)

(14)

With this time and the value of calculated in (4) we can finally calculate the total time :

(15)

(16)