you must design a runway that allows planes to reach a ground speed of 65 m/s before they can take off. If the planes accelerate at 2.5m/s/s, what must the minimum length of the runway be?

  d = 845 m

Explanation:

This is an exercise in kinematics, specifically accelerated motion, let's use the equation

         v² = v₀² + 2 a d

since airplanes start from rest their initial velocity is zero

         v² = 2ad

         d = v2 / 2a

let's calculate

         d = 65² / (2 2.5)

         d = 845 m

this is the minimum distance from the track

force is mass*acceleration.

we have a very small mass: 11.4*0.001 kg

if we want 0.035n of force, we need an acceleration:

0.035 = 11.4*0.001*a

a = 0.035/(11.4*0.001) m/s^2