Let us write down the equation of traveled distance for the uniformly accelerated motion:
[tex]s=s_0+v_0t+\frac{at^2}{2}[/tex]
In our case [tex] s_0=0;v_0=0[/tex]. We assume that plane started accelerating from rest.
We then get this equation:
[tex]s=\frac{at^2}{2}[/tex]
Now we also know the final velocity of a plane:
[tex]v=a\cdot t[/tex]
We can now solve our problem using those two equations:
[tex]v=a\cdot t\\
s=\frac{at^2}{2}\\
t=v/a\\
s=\frac{a}{2}(\frac{v}{a})^2\\
s=\frac{a}{2}\cdot \frac{v^2}{a^2}\\
s=\frac{v^2}{2a}\\
a=\frac{v^2}{2s}[/tex]
When we plug in the number we get [tex]a=2.25\frac{m}{s^2}[/tex].
