Question

What percentage of the takeoff velocity did the plane gain when it reached the midpoint of the runway? a plane accelerates from rest at a constant rate of 5.00 m/s2 along a runway that is 1800 m long. assume that the plane reaches the required takeoff velocity at the end of the runway. what is the time tto needed to take off?

Answer 1

When is at the end of the runway the velocity of the plane is given by the equation $vf^{2}=0+2*a*s$    where s=1800 m is the runway length. Thus
$vf^{2}=2*5*1800=18000 (m/s)^{2}$      
$vf =134.164 (m/s)$  

At half runway the velocity of the plane is
$v^{2}=2*5* \frac{1800}{2}=9000 ( \frac{m}{s} )^{2}$ 
$v= \sqrt{9000}=94.87 ( \frac{m}{s})$

Therefore at midpoint of runway the percentage of takeoff velocity is
‰$P= \frac{v}{vf}= \frac{94.87}{134.164}=0.707$