Question

An airplane acceleration is 3m/s^2. The minimum take-off speed is 102 m/s. The minimum runway length is ____ meter.

Answer 1

The airplane starts form rest, then accelerates by rate of
`3m/s^2` until it reaches 102m/s at the end of the runway. so we have:

`Vo=0m/s\\Vf=102m/s\\a=3m/s^2\\\\`

From the equations of uniformly accelerated motion (since the airplane's acceleration is uniform)
`'Vf^2=Vo^2+2aS' \\` is compatible to find the minimum runway length (S).

`Vf^2=Vo^2+2aS\\Vf^2-Vo^2=2aS\\S=Vf^2-Vo^2/2a\\`

`S=((102m/s)^2-(0m/s)^2)/2m/s^2\\S=(10404m^2/s^2-0m^2/s^2)/2m/s^2\\S=(10404m^2/s^2)/2m/s^2\\S=5202m`