If the jet plane is taking off, we know that initially the plane isn't moving (initial speed is zero, Vo=0m/s), the final speed (the one the plane needs to takeoff is 75m/s (Vf=75m/s), we need to verify if accelerating at a rate of 1.3m/s^2, the plane can reach the takeoff speed in a distance of 2.5km (the length of the runway). To do that we calculate the distance that will take to reach that speed, like the following:
[tex]2*a*d=Vf^{2} -Vo^{2}[/tex] this is the formula we are using, where "a" is the acceleration and "d" is the distance we are going to calculate.
[tex]d=\frac{Vf^{2} -Vo^{2} }{2*a}[/tex]
[tex]d=\frac{(75m/s)^{2} -(0m/s)^{2} }{2*(1.3m/s^{2}) }[/tex]
[tex]d=\frac{5625m^{2}/s^{2} }{2.6m/s^{2} }[/tex]
d=2146.63m=2.146km.
The plane needs 2.146km to reach the takeoff speed, and the runway has 2.5km, so the plane will be able to use the runway safety.
