Question

An aircraft has a liftoff speed of 53 m/a what is the minimum constant acceleration an airplane must have to reach that takeoff speed if the runway is only 420 m long

Answer 1

`a=3.34\ m/s^2`

Step-by-step 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
`v_o=` initial speed,
`v_f=` final speed, a= acceleration, x= distance, then, the scalar equation between them is

`v_f^2=v_o^2+2ax`

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
`v_f=53`,
`v_0=0`, x=420:

`\displaystyle a=(v_f^2-v_0^2)/(2x)`

`\displaystyle a=(53^2-0^2)/(2(420))`

`\boxed{a=3.34\ m/s^2}`