Question

A certain aircraft has a liftoff speed of 127 km/h.

(a) What minimum constant acceleration does the aircraft require if it is to be airborne after a takeoff run of 277 m?

Answer 1

Let us write down the equation of traveled distance for the uniformly accelerated motion:

`s=s_0+v_0t+(at^2)/(2)`
In our case
`s_0=0;v_0=0`. We assume that plane started accelerating from rest.
We then get this equation:

`s=(at^2)/(2)`
Now we also know the final velocity of a plane:

`v=a\cdot t`
We can now solve our problem using those two equations:

`v=a\cdot t\\ s=(at^2)/(2)\\ t=v/a\\ s=(a)/(2)((v)/(a))^2\\ s=(a)/(2)\cdot (v^2)/(a^2)\\ s=(v^2)/(2a)\\ a=(v^2)/(2s)`
When we plug in the number we get
`a=2.25(m)/(s^2)`.