The fastest time ever run at Pikes Peak is 7 minutes and 57 seconds. The course is 12.42 miles long and has 156 turns. If we removed all the curves, making it a straight line from top to bottom. How quickly a car reach the top if:
Your cars top speed is 203 mph
Has a peak acceleration of over 1g but will accelerate at an average of .091g (2.93ft/s2).
what difference does the slope make?
Starting from zero, v = at
so, if we peak out at 203 mi/hr (297.73 ft/s) it will take 101.62 seconds
The distance traveled at that point will be s = 1/2 at^2 = 15128.5 ft = 2.87 miles
At the top speed, the remaining 9.55 miles will take 169.44 seconds
Total time: 271 seconds, or 4 min 31 sec.
Forgot to note. Traveling at a 6.4% slope
u going uphill..thats why the slope has to come into play
To calculate the time it would take for a car to reach the top of Pikes Peak without any curves, we can use the following steps:
Step 1: Convert the distance from miles to feet.
12.42 miles = 12.42 * 5280 feet = 65,449.6 feet
Step 2: Calculate the time it takes to reach the top using the average acceleration and top speed.
First, we need to find the time it takes to reach the top with constant acceleration using the following formula:
time = square root of [2 * distance / acceleration]
Using the given acceleration of 2.93 ft/s², we can calculate the time as follows:
time = square root of [2 * 65,449.6 / 2.93]
time = square root of [44,775.136]
time = 211.79 seconds
Step 3: Convert the time from seconds to minutes and seconds.
There are 60 seconds in a minute, so we divide the total time by 60 to get the minutes and seconds:
211.79 seconds / 60 = 3 minutes and 31.79 seconds
Therefore, if there were no curves on Pikes Peak, it would take approximately 3 minutes and 31.79 seconds to reach the top with a top speed of 203 mph and an average acceleration of 0.091g.