During takeoff, the takeoff run of the aircraft lasts 25 seconds. Determine the distance traveled by the airplane along

During takeoff, the takeoff run of the aircraft lasts 25 seconds. Determine the distance traveled by the airplane along the runway if, after passing 3/4 of the takeoff run, the airplane acquired a speed of 51 m / s.

Let the path traveled by the plane along the runway be S = x. Knowing that after passing (3/4) of the take-off run S1 = (3/4) ∙ x, the plane acquired a speed v = 51 m / s, we can express the acceleration with which the plane was accelerated. a = (v ^ 2) / (2 ∙ S1) = (v ^ 2) / (2 ∙ (3/4) ∙ x) = 1734 / x. Since the takeoff run of the aircraft lasted t = 25 s, the path covered by the aircraft along the runway can be found by the formula S = (a ∙ t ^ 2) / 2, we get the equation: x = ((1734 / x) ∙ 25 ^ 2) / 2; x = 736.12 m; S = 736.12 m.
Answer: the distance traveled by the plane along the runway was 736.12 m.