An engineer is deigning the runway for an airport. Of the planes that will use the airport, the lowest acceleration rate is like to be 3 m/s^2. The take off speed for this plane will be 65 m/s. Assuming this minimum acceleration, what is the minimum allowed length for the runway?
We suppose the acceleration is constant over time , hence the motion of the plane is uniform accelerated. if `a = constant` the equation relating the initial and final speed with the space is
`V^2 = V_0^2 +2*a*s`
The data from text are `V =65 m/s` , `V_0 =0 m/s` , `a =3 m/s^2` .
Therefore the minimum allowed length for the runway is
`s = V^2/(2*a) = 65^2/(2*3) =704.167 m`