An aircraft has a liftoff speed of 33 m/s. What minimum constant acceleration does this require if the aircraft is to be airborne after a take-off run of 240 m?
Show your work.
Answer (2)
We will use simple formula for velocity with constant acceleration. v = v 0 + a t and formula for path x = x 0 + v 0 t + 2 1 a t 2 where: v0 - initial velocity a - constant acceleration t- time x - path x0 - initial position v0, and x0 are equal to 0 in this case, so we can simplify our formula to v = a t and x = 2 1 a t 2 We can modify first formula to get time t = a v and substitute it to second formula. x = 2 1 ∗ a a 2 v 2 = 2 1 a v 2
Now we can find acceleration a = 2 1 x v 2 = 2.27 m/s
The minimum constant acceleration required for the aircraft to reach a liftoff speed of 33 m/s over a distance of 240 m is approximately 2.27 m/s². We used the kinematic equation v 2 = v 0 2 + 2 a x to find this value. The initial speed was zero, and we calculated the acceleration necessary to achieve the desired speed within the given distance.
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