Question

An airplane needs to reach a velocity of to take off. On a runway, what is the minimum acceleration necessary for the plane to take flight?

Answer 1

we need the following info:

minimum take off speed
maximum take off roll (runway length)

v^2 = u^2 +2as

v is take off speed
u = 0
a= acceleration
s is take off distance (max take off roll or runway length)

Answer 2

call runway length d
then if starting from rest at one end with constant acceleration a we must reach speed s in distance d:
d = (1/2) a t^2
s = a t
or t = s/a, time rolling on runway
so
d = (1/2) a s^2/a^2
or
d = (1/2) s^2/a
so
a = s^2/(2d)

Answer 3

@damonc2
The variables oyu have used are not commonly used in this field.

u or v0 is used for initial speed
v or v1 used for final speed

(s is often used for distance, as in my equations above)

it is quite confusing to see s=at.
the full equation is v = u +at (but u=0 in this case)