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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.

Sagot :

We will use simple formula for velocity with constant acceleration.
[tex]v=v0+at[/tex] and formula for path [tex]x=x0+v0t+ \frac{1}{2}a t^{2} [/tex]
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
[tex]v=at[/tex] and [tex]x= \frac{1}{2}a t^{2} [/tex]
We can modify first formula to get time
[tex]t= \frac{v}{a} [/tex] and substitute it to second formula.
[tex]x= \frac{1}{2}*a \frac{ v^{2}}{ a^{2} } = \frac{1}{2} \frac{ v^{2} }{a} [/tex] 
Now we can find acceleration
[tex]a= \frac{1}{2} \frac{ v^{2} }{x} =2.27[/tex] m/s 
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