Answer:
[tex]a=3.34\ m/s^2[/tex]
Explanation:
Constant Acceleration
It refers to those cases where the change of the velocity is the same over time, i.e. the velocity changes same quantities in same times. If we set [tex]v_o=[/tex] initial speed, [tex]v_f=[/tex] final speed, a= acceleration, x= distance, then, the scalar equation between them is
[tex]v_f^2=v_o^2+2ax[/tex]
The aircraft needs to reach a liftoff speed of 53 m/s assumed it starts from rest and has only 420 meters to reach that speed. Let's compute the acceleration by solving the above equation for a, with [tex]v_f=53[/tex], [tex]v_0=0[/tex], x=420:
[tex]\displaystyle a=\frac{v_f^2-v_0^2}{2x}[/tex]
[tex]\displaystyle a=\frac{53^2-0^2}{2(420)}[/tex]
[tex]\boxed{a=3.34\ m/s^2}[/tex]
