Question

an aircraft has a liftoff speed of 53 m/s. 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:

Accelerated Motion

It refers to the motion of objects in which velocity is not constant over time. If the change of the velocity occurs at the same rate, then we say it's uniformly accelerated. Being
`v_o`= initial speed,
`v_f`= final speed, a= constant acceleration, x= distance traveled

Then, the scalar relation between them is

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

The aircraft needs to reach a liftoff speed of 53 m/s from rest (assumed) having only 420 meters to do so. We can compute the acceleration by solving for a

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

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

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