An airplane must reach a speed of 240.5 mi/h in order to take off. If the runway is 571.5 m long, what is the minimum value of the acceleration that will allow the airplane to take off successfully?

To find the minimum value of acceleration that will allow the airplane to take off successfully, we need to use the kinematic equation relating acceleration, initial velocity, final velocity, and displacement:

v^2 = u^2 + 2*a*s

Where:
v = final velocity
u = initial velocity
a = acceleration
s = displacement

First, let's convert the given values to the appropriate units:
240.5 mi/h = (240.5 * 1609.34 m) / (1 h * 3600 s) = 107.674 m/s
571.5 m

Now, we need to apply the kinematic equation:
107.674^2 = 0 + 2*a*571.5

Simplifying the equation:
11624.18 = 1143*a

To find the minimum value of acceleration, we rearrange the equation to solve for a:
a = 11624.18 / 1143

Evaluating the expression:
a ≈ 10.18 m/s^2

Therefore, the minimum value of acceleration that will allow the airplane to take off successfully is approximately 10.18 m/s^2.