Question

An aircraft has a liftoff speed of 33 m/s. what minimum constant acceleration does this require if the aircraft is to be airborne after a take-off run of 240m? show work.

Answer 1

We will use simple formula for velocity with constant acceleration.

`v=v0+at` and formula for path
`x=x0+v0t+ (1)/(2)a t^(2)`
where:
v0 - initial velocity
a - constant acceleration
t- time
x - path
x0 - initial position
v0, and x0 are equal to 0 in this case, so we can simplify our formula to

`v=at` and
`x= (1)/(2)a t^(2)`
We can modify first formula to get time

`t= (v)/(a)` and substitute it to second formula.

`x= (1)/(2)*a ( v^(2))/( a^(2) ) = (1)/(2) ( v^(2) )/(a)`
Now we can find acceleration

`a= (1)/(2) ( v^(2) )/(x) =2.27` m/s