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 $x=x0+v0t+ \frac{1}{2}a t^{2}$
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 <u />$x= \frac{1}{2}a t^{2}$
We can modify first formula to get time
$t= \frac{v}{a}$ and substitute it to second formula.
$x= \frac{1}{2}*a \frac{ v^{2}}{ a^{2} } = \frac{1}{2} \frac{ v^{2} }{a}$ 
Now we can find acceleration
$a= \frac{1}{2} \frac{ v^{2} }{x} =2.27$ m/s