According to Richard Graham in "SR-71 Revealed: The Inside Story", the Lockheed SR-71 Reconnaissance plane accelerates from a standing start to a speed of Mach 3 (3 times the speed of sound) "in about 14 minutes". (During that time it also climbs to an altitude of about 70,000 feet, so the acceleration is not as impressive as you might otherwise expect.) Assuming that the time is exactly 14 minutes, and the speed of sound is 1100 feet per second, this is an average acceleration of ? feet per second squared. Assuming that the acceleration is constant, during that time your SR-71 covers a distance of ? miles.
1) a(average) = (v2 - v1) / (t2 - t1) = ((3300 - 0) / (840 - 0)) = 3.93m/s^2
2)….
2) Take the integral of a(t) to get v(t) and then proceed to integrate v(t) to get s(t). Once you got s(t), which is (3.93t^2 /2) from (840 to 0) plug in 840 to into this equation to get 3.93(840)^2 /2 = 1386504 feet but you want miles so... you then proceed to divide by 5280 to get 262.5 miles, which is the answer!
To find the average acceleration of the SR-71 during its acceleration phase, we need to determine the change in velocity and the time taken. Given that the time is exactly 14 minutes and the speed of sound is 1100 feet per second, we can first convert the time to seconds:
14 minutes * 60 seconds/minute = 840 seconds.
Now, to calculate the change in velocity, we need to find the difference between the final velocity and the initial velocity. The final velocity is Mach 3 times the speed of sound, which is:
Mach 3 * 1100 feet/second = 3300 feet/second.
The initial velocity is 0 feet/second since it starts from a standing start. Therefore, the change in velocity is:
3300 feet/second - 0 feet/second = 3300 feet/second.
Finally, we can calculate the average acceleration using the formula:
Average Acceleration = Change in Velocity / Time.
Average Acceleration = 3300 feet/second / 840 seconds.
Now we can calculate the average acceleration of the SR-71 during its acceleration phase.