If an airplane needs a minimum of 148 m/s to take off, and it accelerates at 3 m/s^2, how long should the runway be so that it can take off at this minimum speed?

Assuming it takes off from rest, the runway should have length x such that

(148 m/s)² - 0² = 2 (3 m/s²) x

which follows from the formula,

v² - u² = 2 a ∆x

(where u is initial speed and v is final speed; the other two's significance should be obvious)

Solve for x :

x = (148 m/s)² / (2 (3 m/s²))

x ≈ 3650.67 m